Why Peter over John as First Pope?

That’s an interesting but ultimately speculative question. It’s not something our Lord Jesus Christ revealed to us regarding his choosing St. Peter vs. St. John as the first Pope in carrying out his divine plan (Matt. 16:18-19).

Part of our Lord’s becoming human was to illustrate how closely he identifies with us in redeeming us from sin and offering us eternal life. Jesus didn’t strictly need to become man to save us, but the Father sent—and Jesus agreed—to fittingly illustrate the ugliness of sin and how much God loves us (see John 3:16-17).

In a different way, perhaps Jesus chose Peter to give us all hope as his disciples. Peter wasn’t necessarily the most virtuous, particularly at first, as Jesus had to correct him for initially opposing his Paschal Sacrifice (Mt. 16:21-23). And after Peter denied Jesus three times, Jesus forgave Peter and restored him to right relationship with him (Matt. 26:69-75; John 21:15-17).

And so Peter moved forward faithfully in the Lord. In that light, perhaps (in part) Peter’s selection was to give us hope that we can count on merciful Lord’s love and thus repent when needed—and not despair—and continue to grow in fellowship with Our Lord and our fellow disciples, particularly those closest to us.