pssst...the word "Catholic" simply means UNIVERSAL. So, where a bishop (or presbyter or elder...the NT uses those words interchangibly) appears, says St. Ignatius, the Church UNIVERSAL is--I have no problem with that, but I'm not about to join the body under the control of a Bishop of Rome.
I find it very sad that the word "catholic," the most universal, unifying, and (rightly) ecumenical word there is, is used by those with an odd loyalty to a particular capital city (which St. John and St. Peter too referred to as "Babylon"...not a great compliment to say the least) and her bishop.
I am a happy part of the Church catholic, but not under the authority (supposed proven by revisionist history and proof-texts) of Rome's bishop; Christ needs no vicar, and is quite able to lead the Church Himself.
Anyone interested really should read the New Testament book of Acts--as I just did. Although he is certainly a highly respected leader, there is no evidence of any kind of papal authority exercised by St. Peter. If anyone is the chief elder in the Church it is St. James (see Acts 15...about the first ecumenical council of the Church). Most of the book is about St. Paul as well....who at one time even publicly rebuked Peter, as an EQUAL, not as a papal subject.(Gal. 2:11-ff) Clearly the primitive church had a counciliar form of government, looking to Christ through the Holy Spirit to lead--using bishops and elders for sure, but NOT the kind of hierarchical structure of the Roman church today.
I hate to break this to you, but the ancient city of Rome did not include the side of the Tiber where the Vatican is located.