Matthew 16 has another disagreement between Jesus and the Pharisees (and the Sadducees as a bonus) about showing signs. Yeah, there's some harsh language, but I think Jesus makes a good point; there have already been quite a number of signs performed by Jesus, even in front of them, and as I said back in chapter 12 when there was a similar exchange, Jesus isn't there to perform tricks for anybody.
The SAB asks of verse 17 "How did Peter find out that Jesus was the Messiah?" I can see why the SAB might consider this verse a contradiction with John 1:41, but I don't think it is. Yes, Andrew told Peter that Jesus was the Messiah, but I think Jesus is saying that Peter's finally accepting this truth was a spiritual matter. I mean, I could tell any reader of my blog that Jesus was the Messiah until the second coming, but I think there needs to be something spiritual that "reveals" the truth of this to your heart, so to speak.
Verses 18-19 are open to interpretation, but it does seem on the face of it that this may be Jesus stating that Peter is to be the leader of the church; sure, you can call him the first Pope if you'd like to put it that way, I have no problem with it. Some have suggested that "this rock" that Jesus speaks of is not Peter himself, but Peter's statement of faith that Jesus is the Messiah, and there's some wiggle room for such an interpretation. As for what "the gates of hell shall not prevail against it" means, I can't say; as the SAB points out, the Catholic church has had a spotty history, so it's certainly not incorruptible. As a side note, I'd like to point out that protestants who like to wave aside such ugly history with declarations of, "Of, but that's the Catholic church!" can't really take such an easy out when it comes to history of the church before the protestant reformation, as until that point in most of Europe the Catholic church was synonymous with Christianity. Just a thought.
Almost immediately after praising Peter, Jesus ends up having to rebuke Peter trying to rebuke him over his coming death. Harsh, but then even a Catholic will tell you that being Pope doesn't make you perfect. (Remember also that "satan" means "adversary", and Peter was certainly being adversarial at that moment.)
In verse 25, which the SAB marks as unjust and absurd, Jesus says that one should lose one's life in order truly find it. No I don't think Jesus is saying that you should kill yourself, but is suggesting that people should put aside their personal desires and seek Jesus first. Jesus goes on to speak of how God "will reward each according to his works." and asks whether salvation is by faith alone. I think I already addressed this a few chapters back, but my view is that while salvation is by faith, in the afterlife, there are different rewards according to the works that a person of faith has done.
At the end of this chapter, Jesus makes a very strange statement, "There be some standing here, which shall not taste of death, till they see the Son of man coming in his kingdom." The SAB interprets this as a statement about the end of the world, which is not unreasonable, except seeing as nearly 2,000 years have passed since Jesus made the statement and now, and we don't know of any 2,000-year-olds, this would seem to be a problem. The only solution that I know of is that some have suggested the event Jesus is talking about is not the second coming, but the strange, miraculous event that Matthew talks about in the very next chapter, known as the Transfiguration.