Biblical origin of the Papacy
The Bible teaches what the Catholic Church teaches
We are all called by Jesus Christ, the true God, one in substance with the Father and the Holy Ghost, to believe in Him and in the Church He sent after Himself, and which is protected by the same Holy Ghost. Further, we are called to live in accordance with the morality of Jesus Christ, as taught by His Church, but admonished to not unite with false worship and false worshippers.
Corinthians 6:15: "And what concord hath Christ with Belial? Or what part hath the faithful with the unbeliever?"
But many who believe themselves to be traditional Catholic are in fact following the Vatican II sect directly, or indirectly through attendance at schismatic sects like the SSPV who continue to allow communion with the modern antipopes. Additionally many of their ideas regarding the indefectibility of the Church, which surely formed some part of their decision making process in this matter, rely on teachings from Leo XIII. The problem with this is Leo XIII publicly taught a clear deviation from the universal truth that only those who have entered the Church by baptism are counted among the sons and daughters of God.
Masoniclibrary.org: "A Mason believes in the Fatherhood of God requiring that His will be done and that He guides his life. A Mason believes in the great worth of the individual. Great worth not relating to wealth, position or power, but recognising that each individual is a human being, a creation of God, and a person of value. A Mason believes that each individual is under the Fatherhood of God."
Antipope Leo XIII, Satis Cognitum, #3, The Church Always Visible: "But since the Church is such by divine will and constitution, such it must uniformly remain to the end of time. If it did nor, then it would not have been founded as perpetual, and the end set before it would have been limited to some certain place and to some certain period of time; both of which are contrary to the truth. The union consequently of visible and invisible elements because it harmonizes with the natural order and by God's will belongs to the very essence of the Church, must necessarily remain so long as the Church itself shall endure. Wherefore Chrysostom writes: "Secede not from the Church: for nothing is stronger than the Church. Thy hope is the Church; thy salvation is the Church; thy refuge is the Church. It is higher than the heavens and wider than the earth. It never grows old, but is ever full of vigour. Wherefore Holy Writ pointing to its strength and stability calls it a mountain" (Hom. De capto Eutropio, n. 6)."
The indefectibility of the Church, is most certainly not what Leo XIII would have us believe, in his obvious attempt to groom present and future generations to accept not only the subtle machinations of insidious heretical drops of poison, such as this "God the Father of all" heresy, but to remain tethered to a vessel bound for the seas of indifferentism and moral corruption, unto inevitable ruin when this heresy reaches the culmination of its expression at Assisi in the idolatrous 1986 prayer meeting with the world religions.
For those who have eyes to see, let them see.
God created seven sacraments, but those only two sacraments required for Catholics to exist in every age are the same two sacraments that do not absolutely require ordained priests as their ministers. Baptism and matrimony, the two sacraments founded by God, the first which can be administered by anyone who can speak and pour water, and the second which is administered by the spouses themselves with a priest only as witness. Even without priests, we are still able to approach God as his children through baptism and raise children for him through Matrimony. This is consonant with the notion that even the the end of time, Christ will be with us, as Christ is only truly with those who are baptized, and in a state of grace, though he draws the sinful and faithless by grace.
In this way, the infallibility of the pope and the indefectibility of the Church are not at all the same thing, as some sects would have it, and it is in fact to the detriment of your soul that you continue to receive sacraments from heretic or schismatic priests who have this heresiarch, and/or any of his successors as one of the historical popes. That is what I believe, for all the stated reasons above and in the links provided above and below: