That's not what Jesus said.
If any Apostle were to be considered more influential with the early church.....a name other than Paul would be questionable
Paul himself publicly acknowledged the subordination of his authority to Peter and James.
Influence and authority are two different things - that's why two different words are used to describe them.
Peter was only given the responsibility to the House of Israel
False, as Cornelius shows.
He did not evangelize Cornelius as he (Cornelius) was already a God fearing man
Plenty of people in the Gentile world of the Mediterranean were God-fearers - i.e. they acknowledged the God of Abraham, Isaac and Jacob as the one true God.
But they did not know about His Son, and therefore they needed to be evangelized. Cornelius was just such a man.
This is also why Peter never goes to Rome.
Peter, of course, died in Rome after ministering there. His presence in Rome is attested by his own words.
Chapter & Verse?
Paul himself publicly acknowledged the subordination of his authority to Peter and James.
Chapter & Verse?
False, as Cornelius shows.
Peter was not sent to evangelize Cornelius. Cornelius was already a god fearing man. He was directed to evangelize the House of Israel.
Plenty of people in the Gentile world of the Mediterranean were God-fearers - i.e. they acknowledged the God of Abraham, Isaac and Jacob as the one true God.
Correct....and this was Paul's task....to bring the "Good News" to these folks. Peter was instructed to go to the Israelites and "Not to go to the Gentiles" [Matthew 10:5-6].
Peter, of course, died in Rome after ministering there. His presence in Rome is attested by his own words.
Peter never set foot in Rome. There was a "Simon" in Rome about that time....but it was not Simon Peter. Justin Martyr was the first "Church Father" to catalog the early events of Rome and he frequently mentions Simon Magus and his deeds. He never mentions Simon Peter. Do you consider this odd? After all....Justin wrote early in the second century....not too far removed from the actual events themselves! Peter had been in Babylon....as The Lord had instructed to be.