I understand the promises made to Peter in Mathew 16 and to the apostles as a whole in Mathew 18, but what I would like someone to explain is the Church teaching behind this concept: When Jesus tells the apostles he will send the Holy Spirit down to them and prevent them from saying untruths and essentially make them unfallible, how do we know He intended that to be passed down through apostolic succession?
From the Catechism of the Catholic Church:
**1558 **"Episcopal consecration confers, together with the office of sanctifying, also the offices of teaching and ruling. . . . In fact . . . by the imposition of hands and through the words of the consecration, the grace of the Holy Spirit is given, and a sacred character is impressed in such wise that bishops, in an eminent and visible manner, take the place of Christ himself, teacher, shepherd, and priest, and act as his representative (in Eius persona agant)."37 "By virtue, therefore, of the Holy Spirit who has been given to them, bishops have been constituted true and authentic teachers of the faith and have been made pontiffs and pastors."38
Also see 1 Timothy 4:14. In fact, the letters to Timothy demonstrate apostolic succession perfectly.
Protestants argue He was just talking to the apostles alone and not to the Church itself…So how does the Church react to this?
Interestingly, we will also say that Christ spoke to the Apostles alone, while other Protestants argue that anything Jesus said to the Apostles also applies to all members of the Church.
In fact, Christ spoke to and conferred the power upon the Apostles alone, who then working in the person of Christ conferred the power upon others, such as Timothy.
I know Jesus says the gates of hell will not prevail against the Church, but that doesn’t promise infallibility necessarily. There has to be a better argument than just that. Help on this would be much appreciated!
You are right, and I think that interpretation is kind of bogus even though I am Catholic. The Church offers an official interpretation. From the Catechism of the Catholic Church:
**552 **Simon Peter holds the first place in the college of the Twelve;283 Jesus entrusted a unique mission to him. Through a revelation from the Father, Peter had confessed: “You are the Christ, the Son of the living God.” Our Lord then declared to him: "You are Peter, and on this rock I will build my Church, and
the gates of Hades will not prevail against it."284 Christ, the “living Stone”,285 thus assures his Church, built on Peter, of victory over the powers of death. Because of the faith he confessed Peter will remain the unshakable rock of the Church. His mission will be to keep this faith from every lapse and to strengthen his brothers in it.286
And further:
834 Particular Churches are fully catholic through their communion with one of them, the Church of Rome "which presides in charity."315 "For with this church, by reason of its pre-eminence, the whole Church, that is the faithful everywhere, must necessarily be in accord."316 Indeed, "from the incarnate Word’s descent to us, all Christian churches everywhere have held and hold the great Church that is here [at Rome] to be their only basis and foundation since, according to the Savior’s promise, the gates of hell have never prevailed against her."317