In many ways, Todoroki Touya and Bakugou Katsuki are similar people. Not just through their quirks, but also by personality. Both of them were cheerful but ambitious boys with a great deal of insecurities surrounding their self worth. Both of these boys were told they had the perfect quirk, only to be thrown away when they were no longer perfect.
The difference is the timing and severity to which this process happened. For Katsuki, he was told he was perfect throughout his childhood until he came to UA. However, this was never enough to make him truly confident in himself. Deep down, he knew they were praising his quirk, not him. Therefore, as he got older he gained a very shallow understanding of love and compassion. When he finally entered UA, suddenly his former position went up in smoke and he was given a rude awakening in the form of the kidnapping. As we saw in Deku's fight with him, this fall from grace caused a complete mental breakdown on Katsuki's part. Everything he believed to be true had now been called into question thanks to these events. When Katsuki is hurting emotionally, he has a habit of seeking out fights and training to the point of hurting himself.
There's one other character who took a similar fall from grace and had a similar reaction: Touya. Touya was in denial the day he became imperfect, much the same way Katsuki denied no longer being number one. Both started training obsessively, to the point of willfully hurting themselves in order to win. With Katsuki, this aspect is harder to see. However, he blatantly tells All Might that "he'll break himself" in order to win.
However, not only were Touya and Katsuki dealing with these issues, they were also feeling the pressure at school too. We saw clearly in the manga that Katsuki was under pressure to be perfect due to everyone wanting to be a hero. We also learn in a flashback that Touya was facing similar problems, unable to stop thinking about heroes due to his friends discussing them constantly.
When people only praise a child for a specific talent that they have, those children often grow up with self worth issues. They typically have superiority complexes that are caused by low self esteem, as paradoxical as that seems. Due to insecurity, kids like this feel a need to reaffirm their self worth, often aggressively the more bad things happen. Along with this, they often value and rank people by the same metric they themselves were subjected to. In order to move past this problem, these people often have to learn to stop valuing themselves and others based on one specific attribute.
We see this happen with Bakugou Katsuki. As he learns to value other people in a healthy way, his own extreme views begin to lessen. This contrasts sharply with Touya's views, which only worsen and become more twisted as time passes by.
While he's never stated or treated as such, I believe Bakugou Katsuki's ideal villain counterpart is Dabi. They make excellent character foils to one another, and are driven by a very similar "victory at all costs" mindset. Both of them were ultimately talented kids who had to find a new way to survive when their best stopped being good enough.
