Many websites (including this one) have already explained many aspects of the importance of sedevacantism. In this article I'm going to explain why it's of absolute importance for Catholics to adhere to the papacy and how the only option we are left with is sedevacantism in order to remain Catholic.
Let's first consider a Catholics obligation to believe in Vatican I when it states:
SESSION 4 : 18 July 1870
First dogmatic constitution on the church of Christ (Pastor Aeternus)
Chapter 2. On the permanence of the primacy of blessed Peter in the Roman pontiffs
2.) For no one can be in doubt, indeed it was known in every age that the holy and most blessed Peter, prince and head of the apostles, the pillar of faith and the foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Savior and Redeemer of the human race, and that to this day and for ever he lives and presides and exercises judgment in his successors the bishops of the holy Roman see, which he founded and consecrated with his blood .
3.)Therefore whoever succeeds to the chair of Peter obtains by the institution of Christ himself, the primacy of Peter over the whole church. So what the truth has ordained stands firm, and blessed Peter perseveres in the rock-like strength he was granted, and does not abandon that guidance of the church which he once received.
4.) For this reason it has always been necessary for every church–that is to say the faithful throughout the world–to be in agreement with the Roman church because of its more effective leadership. In consequence of being joined, as members to head, with that see, from which the rights of sacred communion flow to all, they will grow together into the structure of a single body .
Chapter 3. On the power and character of the primacy of the Roman Pontiff
2. Wherefore we teach and declare that, by divine ordinance, the Roman Church possesses a pre-eminence of ordinary power over every other Church, and that this jurisdictional power of the Roman Pontiff is both episcopal and immediate. Both clergy and faithful, of whatever rite and dignity, both singly and collectively, are bound to submit to this power by the duty of hierarchical subordination and true obedience, and this not only in matters concerning faith and morals, but also in those which regard the discipline and government of the Church throughout the world.
3. In this way, by unity with the Roman Pontiff in communion and in profession of the same faith , the Church of Christ becomes one flock under one Supreme Shepherd .
4. This is the teaching of the Catholic truth, and no one can depart from it without endangering his faith and salvation.
5. This power of the Supreme Pontiff by no means detracts from that ordinary and immediate power of episcopal jurisdiction, by which bishops, who have succeeded to the place of the apostles by appointment of the Holy Spirit, tend and govern individually the particular flocks which have been assigned to them. On the contrary, this power of theirs is asserted, supported and defended by the Supreme and Universal Pastor; for St. Gregory the Great says: "My honor is the honor of the whole Church. My honor is the steadfast strength of my brethren. Then do I receive true honor, when it is denied to none of those to whom honor is due."
6. Furthermore, it follows from that supreme power which the Roman Pontiff has in governing the whole Church, that he has the right, in the performance of this office of his, to communicate freely with the pastors and flocks of the entire Church, so that they may be taught and guided by him in the way of salvation.
8. Since the Roman Pontiff, by the divine right of the apostolic primacy, governs the whole Church, we likewise teach and declare that he is the supreme judge of the faithful, and that in all cases which fall under ecclesiastical jurisdiction recourse may be had to his judgment. The sentence of the Apostolic See (than which there is no higher authority) is not subject to revision by anyone, nor may anyone lawfully pass judgment thereupon. And so they stray from the genuine path of truth who maintain that it is lawful to appeal from the judgments of the Roman pontiffs to an ecumenical council as if this were an authority superior to the Roman Pontiff.
Chapter 4: On the infallible teaching authority of the Roman Pontiff
2. So the fathers of the fourth Council of Constantinople, following the footsteps of their predecessors, published this solemn profession of faith: "The first condition of salvation is to maintain the rule of the true faith. And since that saying of our lord Jesus Christ, You are Peter, and upon this rock I will build my Church, cannot fail of its effect, the words spoken are confirmed by their consequences. For in the Apostolic See the Catholic religion has always been preserved unblemished, and sacred doctrine been held in honor. Since it is our earnest desire to be in no way separated from this faith and doctrine, we hope that we may deserve to remain in that one communion which the Apostolic See preaches, for in it is the whole and true strength of the Christian religion."
What is more, with the approval of the second Council of Lyons, the Greeks made the following profession: "The Holy Roman Church possesses the supreme and full primacy and principality over the whole Catholic Church. She truly and humbly acknowledges that she received this from the Lord himself in blessed Peter, the prince and chief of the apostles, whose successor the Roman Pontiff is, together with the fullness of power. And since before all others she has the duty of defending the truth of the faith, so if any questions arise concerning the faith, it is by her judgment that they must be settled."
Then there is the definition of the Council of Florence: "The Roman Pontiff is the true vicar of Christ, the head of the whole Church and the father and teacher of all Christians; and to him was committed in blessed Peter, by our lord Jesus Christ, the full power of tending, ruling and governing the whole Church."
6. For the Holy Ghost was promised to the successors of Peter not so that they might, by his revelation, make known some new doctrine, but that, by his assistance, they might religiously guard and faithfully expound the revelation or deposit of faith transmitted by the apostles. Indeed, their apostolic teaching was embraced by all the venerable fathers and reverenced and followed by all the holy orthodox doctors, for they knew very well that this See of St. Peter always remains unblemished by any error, in accordance with the divine promise of our Lord and Savior to the prince of his disciples: "I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren."
The problem with those who fail to submit to the Roman Pontiff
If Francis I-John XXIII are truly the vicars of Jesus Christ on earth, then according to Vatican I their authority binds on all Catholic consciences and it would be schismatic to reject them. We see over and over again so called traditional Catholics ignoring and ridiculing their pope as if it's a traditional belief to resist a pope. In their case it isn't just over sinful commands but against his ruling authority, his teaching, and while they are so bent on saying they are popes, act as though that is all they care about it. They won't defend them in any other way but will in fact denounce him as though he were the most meaningless man on earth.
When in the history of the Church has a pope ever been resisted on a day to day basis as we see with the so called one today? How is it traditional to preserve tradition by resisting a pope, when traditionally speaking Catholics have always obeyed the pope? How can anybody dare say that he can error and still be the head and teacher of the whole Church? Did not St. Robert Bellarmine say "The Pope is the Teacher and Shepherd of the whole Church, thus, the whole Church is so bound to hear and follow him that if he would err, the whole Church would err." De Romano Pontifice, Book IV, Chapter 3
Could a Council judge a pope if he were a heretic?
There is a common belief among pseudo traditional Catholics that a council will judge and depose a pope. These same people (mostly lay folk) know personally their popes are heretics but to avoid sedevacantism excuse their pope for the bishops and cardinals to decide that for them, when they know that it won't ever happen since a majority of the Vatican II sect Bishops and Cardinals side with Francis and subscribe to Vatican II.
Since Vatican I declared that the pope can be judged by no one, we have a beautiful historical example written by Count Joseph de Maistre in a book called The Pope where he explains how councils are convoked by the pope to settle issues and he alone has the power to assemble them and not the other way around. (Shout out to commenter The Catholic Archive for I found a link to this book off his website).
He states:
Wherever there is a Sovereign, and in the Catholic economy his existence is undeniable, there can be no legitimate assemblies without him, No sooner is his veto pronounced, than the assembly is dissolved, or its co-legislative power suspended; if it resist, their is a revolution.
This very simple and undoubted truth, which can never be shaken, shows in its full light, the extreme absurdity so much discussed: Whether the Pope be above the council, or the council be above the Pope? For it is the same as to inquire, in other words, the Pope be above the Pope or the council above the council?
I firmly believe with Leibnitz, that God has hitherto preserved the truly ecumenical councils from all error contrary to sound doctrine. I believe, moreover, that He will always so preserve them; but since there can be no ecumenical council without the Pope, what signifies the question, whether it be above or inferior to the Pope?
Is the King of Great Britain superior to parliament, or is the parliament above the king? Neither way; but the king and parliament united constitute the legislature or the sovereignty; but there is not an inhabitant of three kingdoms who would not rather have his country governed by a king without a parliament than by a parliament without a king...
To the Sovereign Pontiff alone belongs essentially the right of convoking general councils, which do not exclude the moderate and legitimate influence of sovereigns. He alone is judge of the circumstances which require this extreme remedy. Those who pretend to assign this power to temporal authority, quite overlook the paralogism into which they fell. They suppose an universal and (what is more) everlasting monarchy. They go back without reflecting, to those times when all the mitres in the world could be called together by one scepter only, or two. The Emperor alone, says Fleury, was able to convoke general councils, because he alone could command the bishops to undertake extraordinary journeys. He for the most part defrayed expenses of them, and indicated the place they were to be held in. The Pope confined themselves to asking for these assemblies, and they often asked without obtaining. ( pgs.12-14)
Is sedevacantism just a opinion?
A theological opinion is a position which has faulty and insufficient evidence in its favor, so that you would not be surprised to find out that the opposite is true. Sedevacantism would be a theological conclusion because it is an absolute certainty which can be connected to truths of the Faith in such a way that, if denied, you would have to deny the Faith as well. Therefore, Francis I- John XXIII either are popes or they are not popes because to determine obedience and unity of Faith a person would have to know this, which is precisely why it is an important subject matter. We must know because if we are not following a true pope we would be in danger of schism and if we are following a false pope we would be in danger of believing false doctrine. There is no middle ground and it is a pity that so many so called traditionalist even among some sedevacantist who treat this as though it is just an opinion that can be left up to the individual when unity of faith and government are part of the One true Church from how a Catholic would have to follow it.
The Catechism of the Council Trent explains the importance of Unity when it states:
Unity In Government
The Church has but one ruler and one governor, the invisible one, Christ, whom the eternal Father hath made head over all the Church, which is his body; the visible one, the Pope, who, as legitimate successor of Peter, the Prince of the Apostles, fills the Apostolic chair.
It is the unanimous teaching of the Fathers that this visible head is necessary to establish and preserve unity in the Church. This St. Jerome clearly perceived and as clearly expressed when, in his work against Jovinian, he wrote: One is elected that, by the appointment of a head, all
occasion of schism may be removed. In his letter to Pope Damasus the same holy Doctor writes: Away with envy, let the ambition of Roman grandeur cease! I speak to the successor of the fisherman, and to the disciple of the cross. Following no chief but Christ, I am united in communion with your Holiness, that is, with the chair of Peter. I know that on that rock is built the Church. Whoever will eat the lamb outside this house is profane; whoever is not in the ark of Noah shall perish in the flood...
Unity In Spirit, Hope And Faith
Moreover, the Apostle, writing to the Corinthians, tells them that there is but one and the same Spirit who imparts grace to the faithful, as the soul communicates life to the members of the body. Exhorting the Ephesians to preserve this unity, he says: Be careful to keep the unity of the Spirit in the bond of peace; one body and one Spirit. As the human body consists of many members, animated by one soul, which gives sight to the eves, hearing to the ears, and to the other senses the power of discharging their respective functions; so the mystical body of Christ, which is the Church, is composed of many faithful. The hope, to which we are called, is also one, as the Apostle tells us in the same place; for we all hope for the same consummation, eternal and happy life. Finally, the faith which all are bound to believe and to profess is one: Let there be no schisms amongst you, says the Apostle. And Baptism, which is the seal of our Christian faith, is also one.
Conclusion
If Francis I-John XXIII are true vicars of Jesus Christ since when did popes (like them) pray with Voodooist priests and animists to their false gods, or ever sympathize with Martin Luther and even go as far as saying he didn't really error on justification and that he is a witness of the gospel, or say that the Blessed Virgin Mary was not born a saint, or say that Christ didn't really descend into hell, or say that altar girls enrich the liturgy, or call Eastern Orthodox members and pastors in the Church of Christ, or say Sodomite people were born that way, or say that error has rights, or say the Moslem's worship the same God as Christians, or invite Protestants to construct a liturgy in more conformance with Protestantism, or have ties with the Freemason or global elites?
So much could be added but Our Lord was clear "I am the good shepherd. The good shepherd giveth his life for his sheep. But the hireling, and he that is not the shepherd, whose own the sheep are not, seeth the wolf coming, and leaveth the sheep, and flieth: and the wolf catcheth, and scattereth the sheep: And the hireling flieth, because he is a hireling: and he hath no care for the sheep. I am the good shepherd; and I know mine, and mine know me." (St. John 10: 11-14).