It's not my opinion; it's textual fact. "Why" is irrelevant.
“It’s not my opinion; it’s textual fact”
(Acts 11:19-26) “Now they which were scattered abroad upon the persecution that arose about Stephen travelled as far as Phenice, and Cyprus, and Antioch, preaching the word to none but unto the Jews only. And some of them were men of Cyprus and Cyrene, which, when they were come to Antioch, spake unto the Grecians, preaching the Lord Jesus. And the hand of the Lord was with them: and a great number believed, and turned unto the Lord.”
Notice who is doing the preaching in Antioch. It is those who were scattered due to the persecution; it is not Peter.
22 “Then tidings of these things came unto the ears of the church which was in Jerusalem: and they sent forth Barnabas, that he should go as far as Antioch. Who, when he came, and had seen the grace of God, was glad, and exhorted them all, that with purpose of heart they would cleave unto the Lord. For he was a good man, and full of the Holy Ghost and of faith: and much people was added unto the Lord.”
Notice that the news of people being converted was “news” to the Jerusalem church, so much so, that they sent Barnabas to authenticate it. Now pay close attention. If Peter had started the church, it would not have been “news” to the Jerusalem church and they would not have had to send Barnabas to corroborate what Peter had done since they had already discussed the Cornelius conversion with him.
25 “Then departed Barnabas to Tarsus, for to seek Saul: And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.”
Notice that when Barnabas retrieved Saul and brought him to Antioch, there was now an established growing church.
What the passage shows is that the beginning of the church was with the preaching of the scattered believers; it came as news to the Jerusalem church which sent Barnabas to authenticate it; the church grew while he was there; he went to get Saul and brought him back to the church where they taught for a year. Peter had nothing to do with the church at Antioch. Those are the “textual” facts!