He gave that to all the Apostles. It is called the Apostolic Succession not Peter’s succession. I have to say that this nitpicking on which of the apostles were more favored by Christ sounds more like a wordly quarrel of us here, clerics and lay people, not yet in Heaven, not knowing if we will pass God’s Judgement while ALL the first Apostles are in Heaven. And this one-sided view of the 2000 years history of the Catholic Church does not give justice to the ecclesiastical tradition and ideas promoted that the Church of Rome founded.
I wonder what Saint Peter himself thinks of all this together with his 11 brothers in Christ. The Catholic Church teaches and discusses things in a far more nuanced way than your post.
To the OP - the internet contains a lot of information you can’t check. If this causes you spiritual trouble please stay away from it for a while, I have. If people in real life are nasty to you for being a Catholic pray for them, especially relatives. Don’t take decisions on what people say without examples and sources. Christ is not the result of the sum of everyone’s opinion. Christ is one. Have you experienced His presence in the Catholic Church? If yes, then why fret?