How do Christians justify not being catholic?

[DeistPaladin]

What the title says. Didn't Jesus pretty explicitly state that

And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.

and wouldn't that entail that only the Roman church is the the rightful successor of Jesus? I'm just interested in the rationale of evangelical/protestant Christians behind rejecting this claim.

As others have said, that would actually be the Orthodox Church, which predates Rome's authority. But either way, Protestants reject that authority on the grounds that there was a "early church" that predates the one established by the Roman Empire. 

This "pure, simple, early church" only exists in Christian dreamscapes.

This is the motif of any schismatic church. They don't claim to be rebelling against religious authority. They're "getting back" to a more pure version of what the religion was supposed to be in the first place before it was "corrupted" and that it is the religious authority who are the ones who have strayed from the path. 

So it is with Protestantism.
So it is with Islam.
So it is with Mormonism. 
So it is with Nicene Christianity in general over Judaism. 

Remember that Jesus did not fulfill the roles that the Jewish Messiah was supposed to fulfill. The Jews were expecting a glorious warlord that would lead Israel to ultimate victory, conquering the world. Christians tie themselves into knots trying to reconcile how this peace-and-love hippy that preached a universal religion (supposedly) was the Jewish Messiah. Yet somehow, Christians believe the Jews have gotten it wrong and they should have gotten on the Jesus bandwagon.

I could go into further detail over the personal-relationship-with-Jesus-over-following-the-vicars-of-Christ argument that is the general flavor of Protestantism but you get the idea.