Bakugou's sense of self-worth is built on his superiority to others due to being praised so much for his superior quirk as a kid. As a result, anything that could challenge that superiority is a threat to his entire identity, and so he responds to even minor provocation by getting absolutely pissed off.It's due to his deep-seated insecurities. Bakugon is a jerk because when he was a kid, he was always praised for having such a cool quirk and everyone thought that he was so cool and this triggered his superiority complex, causing him to think that he is better than anyone and everyone.