Gospel of Mary
I became intrigued with the Gospel of Mary when I saw a documentary called, 'The Real Da Vinci Code'. After reading it I wondered if Peter really was jealous of her. See some of the links and say what you think, along with how genuine you believe the writings to be.
For reading:
https://reluctant-messenger.com/gospel-magdalene.htm
LDS related explanation
https://www.meridianmagazine.com/books/040615davin2.html
If the text is accurate... and that is a big 'if', then it may be that Peter wondered what the position of the Apostles was if Mary was used as the instrument to bring knowledge to them. Maybe we can see it like the Bishop's wife counseling us instead of the Bishop himself. Peter, a great man, but was still human and susceptible to certain feelings as he showed many times throughout the Gospels and Acts.