“Think not that I am come to send peace on earth: I came not to send peace, but a sword. For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter in law against her mother in law. And a man's foes shall be they of his own household.”

This is so true

I don't get why would Jesus do that? How is he a Prince of Peace?

This verse only makes sense when you read the whole chapter. Standing alone, it sounds like Jesus came for violent reasons instead of His true reason, to reunite us with His Father. He is sending His disciples out into Isreal and preparing them for the persecution they're about to face. In verse 37, it's cleared up some when he says "Anyone who loves his father or mother (or son or daughter) more than me is not worthy of me. " So I think He's saying He wants us to have a higher priority on following Him than on "keeping the peace" in relationships that try to pull us away from Him. Balance that with "If it is possible, as far as it depends on you, live at peace with everyone." (Romans 12:18) Look at Jesus's life. He made some enemies, but it was always by doing good: healing on the Sabbath, exposing hypocrites who were taking advantage of the poor, reprimanding people for not caring for their own parents, . . . He wants us to be consumed with representing God like He was, even if it makes enemies.