Your error is believing the Roman church dates back to Peter. Apostolic succession is a grand lie. The New Testament developed just as the Old Testament did—over time and by consensus of the saints.
When did the RC Church start? Who founded it?
Who were these saints; how do we know they had authority to compile the New Testament?
Jesus told Peter that he would found a Church with Peter as the rock and that Peter would have the keys to the kingdom of Heaven. Apostolic Succession rests on these keys being handed down from one person to the next. There is nothing in the NT that says they cannot be, nor is there anything that says they can be. So what happens to these keys?
Using Hosea 2, we have that Christians are the New Jews/Israel. The tribe of Judah ruled over all the tribes of Israel. However, due to misbehavior, 10 of the tribes rebelled and formed their own Kingdom. That Kingdom fell to sin. In Isaiah 22, we have the curious case that the key to the House of David can be passed down from generation to generation and that the holder of the key can open a door that none can shut and can shut the same door that none can open.