First off let me start by saying I have no dog in this fight, as you can see by my flair, so I will post an argument, as the mods have demanded, but it will be one from a position of neutrality. I am mostly interested in this because some Christians have told me Catholics are not Christians while Catholics claim to be. Reddit doesn't seem to have much on this based on my searches and the ones I found are all old and barren. My internet searches have only surfaced biased and unchallenged opinions. I will be happy to respond to any reply of of course but please note that I have no ulterior motive here. I have no "gotcha" statement waiting to spring. I will be happy to edit my post depending on the validity/cogency and soundness/strength of your arguments or if I just made a simple error. I might also just reply to your comment.

Here is my argument:

(1) A Christian believes Jesus of Nazareth is the son of God

(2) A Christian believes Jesus Christ is their savior

(3) A Christian follows the teachings of Jesus Christ

(4) A Catholic believes (1),(2) and (3)

(5) Therefore, a Catholic is a Christian

I imagine the problem here will be premise (3) or I am missing something entirely in reference to what it is essential to the title of Christianity. So, what is the problem with premise (3) or what premise am I missing altogether?

edit #1: Given that we have a good sample of responses to go off now, though I don't think I've seen any Protestants yet, lets update the argument a bit. As I suspected, Every denomination interprets Christ's teachings differently and claims to be doing it correctly while the others are not. So catholics claim (3) while others deny Catholics claim (3). This is just the No True Scotsman Fallacy(NTSF). You cannot claim to be a True Christian and claim others false without some sort of evidence that plainly shows your denomination to be Christian while the other is not. One commenter denied the NTSF and claimed the issue to be a semantic dispute. Semantic disputes are not immune to fallacies though and quite often result in fallacies such as NTSF or equivocation.