The Church is indefectible. She can never fail, nor lead astray, nor be led astray. She can never lose the four marks of Her character as a Church: one, holy, catholic, and apostolic. And She will always have a succession of Roman Pontiffs. Each Pope, then, is the head of the Apostolic College as well as the head of the Church.
If the head of the Church, the Roman Pontiff, were ever to go astray, then the Church would have gone astray. Since the Church is indefectible, and the Roman Pontiff is both the head of the Church and the Rock on which She is founded, he also must be indefectible. And this is taught by the First Vatican Council in the sense of the charism of truth and of never-failing faith. No Roman Pontiff can fail in faith, nor teach or commit heresy, nor err gravely in the exercise of the keys of Saint Peter. Thus, the Roman Pontiff must be indefectible, or else the Church would lose Her indefectibility whenever the Roman Pontiff would go astray from the true faith (which is not possible).
But the one Church is also Apostolic. And so, if the body of Bishops, who are the successors to the Apostles, were ever to go astray as a body, then the Church would no longer be Apostolic, or else She could be said to have gone astray with Her Apostles. And so, as long as the body of Bishops remains in communion with and in obedience to the Roman Pontiff, the body of Bishops is also indefectible. For the Roman Pontiff confirms his brethren, the body of Bishops, in the faith. Individual Bishops can go astray, but not the body of Bishops.
For the Church to be indefectible, each Roman Pontiff and the body of Bishops (as a body) must also be indefectible. And therefore, too, no Ecumenical Council can go astray by teaching heresy, nor by any grave error. For the Acts of each Council are approved by the body of Bishops and by the Roman Pontiff.
These things then are indefectible: the Church, the Roman Pontiff, the body of Bishops, and the Ecumenical Councils.
Ronald L. Conte Jr.