Check acts8:14.
If Peter had primacy why would the apostles send him out?
If he was in charge, he would be sending the apostles out.
14 Now when the apostles at Jerusalem heard that Samaria had received the word of God, they sent to them Peter and John, 15 who came down and prayed for them that they might receive the Holy Spirit; 16 for it had not yet fallen on any of them, but they had only been baptized in the name of the Lord Jesus. 17 Then they laid their hands on them and they received the Holy Spirit. Acts 8:14
Peter and John are part of Jesus’ big three, Peter, James, and John. They have seniority over all the Apostles. Just because Peter was send does not negate the fact he isn’t in charge.
Acts 1:13 - Peter is first when entering upper room after our Lord’s ascension. The first Eucharist and Pentecost were given in this room.
Acts 1:15 - Peter initiates the selection of a successor to Judas right after Jesus ascended into heaven, and no one questions him. Further, if the Church needed a successor to Judas, wouldn’t it need one to Peter? Of course.
Acts 2:14 - Peter is first to speak for the apostles after the Holy Spirit descended upon them at Pentecost. Peter is the first to preach the Gospel.
Acts 2:38 - Peter gives first preaching in the early Church on repentance and baptism in the name of Jesus Christ.
Acts 3:1,3,4 - Peter is mentioned first as going to the Temple to pray.
Acts 3:6-7 - Peter works the first healing of the apostles.
Acts 3:12-26, 4:8-12 - Peter teaches the early Church the healing through Jesus and that there is no salvation other than Christ.
Acts 5:3 - Peter declares the first anathema of Ananias and Sapphira which is ratified by God, and brings about their death. Peter exercises his binding authority.
Acts 5:15 - Peter’s shadow has healing power. No other apostle is said to have this power.
Acts 8:14 - Peter is mentioned first in conferring the sacrament of confirmation.
Acts 8:20-23 - Peter casts judgment on Simon’s quest for gaining authority through the laying on of hands. Peter exercises his binding and loosing authority.
Acts 9:32-34 - Peter is mentioned first among the apostles and works the healing of Aeneas.
Acts 9:38-40 - Peter is mentioned first among the apostles and raises Tabitha from the dead.
Acts 10:5 - Cornelius is told by an angel to call upon Peter. Angels are messengers of God. Peter was granted this divine vision.
Acts 10:34-48, 11:1-18 - Peter is first to teach about salvation for all (Jews and Gentiles).
Acts 12:5 - this verse implies that the “whole Church” offered “earnest prayers” for Peter, their leader, during his imprisonment.
Acts 12:6-11 - Peter is freed from jail by an angel. He is the first object of divine intervention in the early Church.
scripturecatholic.com/primacy_of_peter.html