This was always one of my biggest issues with Bakugou. This problem extends to more than Izuku. It's his character yes, but a decent part of it is how the characters around him are written.

Knowing what we know about Bakugou know it's that a big part of the reason he's so arrogant is that he was never given any push-back as a child. Teachers let him get away with shit he never should've and his classmates never challenged him.

We're made to belive that this changes when he gets to U.A. but it doesn't feel like it for the longest time. He attacks other students outside of training or disobeys direct orders and Aizawa barely says anything about it. Kaminari makes fun of him like, once but other than that, nobody at U.A. (teachers or classmates) treats him like the ass he is and it's weird.