Yes, I'm saying Peter was not the founder. If you could go back in time and ask him about the Catholic Church he would have no clue what you were talking about. Heck even the first recorded usage of the word Catholic in 107 AD was a Greek or Latin word to simply describe early Christians being united in their faith; not a term to describe an organized religion.
Admittedly there is no reference in Christianity to the word "catholic" (meaning "universal") until the 2nd century. However if you read the Didache
you see that there are no inconsistencies from the teachings in the Didache to the teachings of the modern catechism. Many historical scholars consider the Didache to be written directly by the apostles and the first catechism.
A critical element in the church is apostolic succession. That is from Jesus-->Peter--->popes--->bishops--->priest though time. It really doesn't matter what this group in apostolic succession calls themselves as long as it is apostolic. Semantics are important but have no bearing on proving or disproving the existence of something. For example, all Christians believe in the trinity, however the word trinity cannot be found in the bible nor was word in existence in the 1st, 2nd, and 3rd centuries.
I also think Peter would totally disagree with you considering he started the Roman church which was one of the Pentarchy right after Jesus died on the cross. In fact, Peter was crucified upside down by the Romans because of his evangelizing in Rome.