Why does everyone think Vegeta is arrogant!?
He is the "Prince of All Saiyans", as he likes to say. All 2-6 of them, depending on where in the show you are and whether you are talking about pure-blood or not. Not really something to brag about dude, you failed your people. Also, he acts like being prince mean he should be the best automatically, even though he clearly is not. He accomplishes nothing himself until the Buu saga when he finally gets over himself.
Its ok to be proud of who you are but not if it is vegana
it is his defining character trait.
did you not the show? he conquered and murdered because he believed his goals mattered more than everyone else's lives because he was a prince, that's why he tried to conquer Earth, that's why he killed all those namekians, that's why he let Cell become perfect and that's why he went Majin in the Buu saga because he believed his noble birth made him better than everyone else and he didn't redeem himself until he realized his arrogance was going to cost the people he loved their lives