What specifically do you not agree with??
First, you imply Jesus did not call Peter "Peter", but rather only referred to him by his birth name. But the scripture says point blank that Jesus called him Peter:
Matthew 16:18
"And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it."
Second, it is clear Peter was the unquestioned leader of the early church, as Mat 16:18 implies.
So, I don’t really agree with your position.
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But, I also don’t agree with the Catholic’s position, for it is clear when Paul was chosen, the scripture explicitly states that Peter was the lead Apostle to the Jews and Paul was the lead Apostle to the Gentiles (Gal 2:7-8). Which is why the first half of Acts is centered on Peter’s ministry and the second half of Acts is centered on Paul’s ministry. And when Paul was having to go before the Jerusalem Council (Acts 15, Gal 2:1-10), he said he didn’t care what position of authority Peter, John, and James held (Gal 2:6,9). Paul was given the gospel through revelation and did NOT learn it from any man (Gal 1:11-12), Paul had direct authority from God that was NOT predicated upon the authority of Peter or anyone else.
The whole purpose of the book of Galatians is to mow down the church leadership in order to show that leadership is fallible. To do this, Paul starts with himself and tells about how he lived in Judaism as a enemy of Christ (Gal 1:13-14) and that it was God who chose Paul, not man (Gal 1:15-24). Paul then, in chapter 2, mows down the supposed brothers who caused the need for the Jerusalem council. Then Paul moves on to Peter, John, and James. Then focuses on Peter's slide back into legalism.
Finally, in chapter 3, after mowing all the leadership down, including himself, Paul turns his guns on the Galatians and asks why they have allowed someone to distort the gospel that was given them.