I’m not here to have a debate, but I’ll say this: I understand where you’re coming from, and I’ve heard that explanation many times before. The sticking point for me, though, is this: How can I know that the Catholic Church has those “legitimate claims to apostolic succession”?
I will use the example of St. Paul…
from 1John 4…6 We are from God, and whoever knows God listens to us; but whoever is not from God does not listen to us. This is how we recognize the Spirit[a] of truth and the spirit of falsehood.
Galatians 1:18 Then after three years I went up to Jerusalem to visit Cephas and remained with him fifteen days.
Galatians 2:2 I went in response to a revelation and, meeting privately with those esteemed as leaders, I presented to them the gospel that I preach among the Gentiles. I wanted to be sure I was not running and had not been running my race in vain.
Paul had a direct revelation from Christ. Yet, from the two passages above, he goes to visit Cephas/Peter and submits himself to Peter. Gal 2: 2 states his purpose…to present his gospel/message to make sure it is in line with the Apostles and what they were handed down from Christ.
Paul submits to the Apostles.
Now look at Acts 13:
1 Now in the church at Antioch there were prophets and teachers: Barnabas, Simeon called Niger, Lucius of Cyrene, Manaen (who had been brought up with Herod the tetrarch) and Saul. 2 While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” 3 So after they had fasted and prayed, they placed their hands on them and sent them off.
Look at verse 3 and see what the Antioch Church elders do…“they placed their hands on them and sent them off.”
This fulfills Romans 10:
14 How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them? 15 And how can anyone preach unless they are sent? As it is written: “How beautiful are the feet of those who bring good news!”[g]
Before Paul and Barnabas went on their first missionary journey, he submits himself to Church authority and are ordained by laying of hands. Then they are sent out to their mission. Paul, by the laying of hands, first becomes an Apostle, he gains apostolic authority, thereby, the Churches he founds have apostolic succession.
This is how it is in the Catholic Church…one does not decide if one is to become a priest…one is sent…by the bishop…which are the successors of the Apostles.
By submitting and obedience to the bishop…we know they are from Christ.
Finally this…Clement of Rome writes this in his Epistle to Corinth…in accordance with the passages above…
42:4 Preaching, therefore, through the countries and cities, they appointed their firstfruits to be bishops and deacons over such as should believe, after they had proved them in the Spirit.
42:5 And this they did in no new way, for in truth it had in long past time been written concerning bishops and deacons; for the scripture, in a certain place, saith in this wise: I will establish their bishops in righteousness, and their deacons in faith.
44:1 Our Apostles, too, by the instruction of our Lord Jesus Christ, knew that strife would arise concerning the dignity of a bishop;
44:2 and on this account, having received perfect foreknowledge, they appointed the above-mentioned as bishops and deacons: and then gave a rule of succession, in order that, when they had fallen asleep, other men, who had been approved, might succeed to their ministry.