You are mistaking a part for the whole. The Roman church is only the diocese of Rome. Rather, the authority of the Apostles headed by Peter is today vested in the entire Catholic Church headed by the Pope as their successors. Nor can you just point to all believers. The refusal of all believers to recognize the legitimate authority established by Jesus Christ has resulted in the division and multitude of churches today.
The Eastern Orthodox would disagree with you. They do not recognize the absolute authority of the pope. Matter of fact, they consider Rome the schismatics.
Both claim to be but have significant doctrinal differences, ones that Rome says damn a man if not adhered to.
So which one is the TRUE Catholic church?