A Catholic apologist named Sean showed me some good insights about the Petros-petra debate from Matthew 16:18. If you have never heard the Protestant claim, it's basically that when Jesus says "You are Peter [Petros] and upon this Rock [petra]" the Greek word Petros means "little pebble" while petra means "big rock". Thus, the Protestant is arguing that Jesus was not identifying Peter with "Rock," but rather contrasting Peter's littleness with the bigness of the Rock (i.e. Jesus). But this argument is simply ridiculous and desperate, and many Protestant scholars have rightly rejected it as well.
The best place to begin tackling this objection is to look at how the Bible uses the term petros. The term petros appears 162 times in the New Testament, with all 162 of those times referring to the Apostle Peter. This is very significant, because just from this data there is no Biblical basis at all that petros ever means "little pebble". In fact, the term petros is simply never used in the NT as a generic term for any rock of any specific size.
So where did the notion that Peter means "little pebble" even come from if not the Bible? Protestant detractors apparently dug up this distinction from a long outdated form of Greek that wasn't even in use at the time of the Apostles (i.e. not Biblical Greek). This detail alone makes the Protestant argument extremely dubious and invalid.
The next term to consider is the Greek term petra. This term is used 16 times in the New Testament, signifying not just "big rock," but something more akin to bedrock, the firmest foundation (Lk 6:48-49). This is significant because it would entail that when Jesus identified Peter as petra, Jesus was not just speaking of a big rock, but rather that Peter is the bedrock upon which the Church is built. This rendering makes far more sense than the Protestant reading of Peter being called a "little pebble," which is actually an insult to Peter after he just professed Jesus to be the Son of God!
The last term to consider is the Greek term lithos, which has a generic meaning of "stone" and is used 60 times in the New Testament. It can refer to small stones that fit in your hand (Mt 7:9; Lk 22:41; Jn 8:59), large rocks the size of boulders (Mt 28:2; Mk 9:42), and even large stone-cut bricks used to build buildings (Mk 13:1-2). Interestingly, the term lithos is also used metaphorically to refer to Jesus (1 Peter 2:6-8), but Protestants would never say that just because lithos is sometimes used to mean "small stone" that Jesus is a "small stone"! Thus, even if petros could mean "little pebble" does not mean we absolutely should take it to mean that when referring to Peter. And if the Protestant thesis were true, we would better expect Jesus to have said to Peter, "You are lithos, and upon this petra," which Jesus didn't do.
The amusing thing is that though Jesus is described as stone and foundation, these same Greek terms apply to Peter as well (1 Peter 2:5; Rev 21:14). So really, there is no good reason why Petros does not mean petra, especially when both are mentioned in the same breath in Matthew 16:18. The only reason why the word ending is different is because petra is a feminine noun, which must be modified to the masculine to fit with the fact Peter was a male. Without that modification, it would be like naming a man Billie (a female name) rather than Billy. And given that Jesus is speaking of Himself as the Builder, "upon this Rock I will build," shows that Jesus is not the referent to Rock here, further strengthening the link between Petros and petra.
To better help Catholics see just how significant this is, they need to know that translating Peter as simply "Rock" actually loses a lot of its force. That's because what Jesus is saying is more akin to "You are Bedrock, and upon this bedrock I will build by Church," or another option, "You are Foundation, and upon this foundation I will build my Church." This brings out the metaphor a lot better and helps people see what Jesus was getting at.