It's more of a case where he feels wronged about everything, so he doesn't want to just run away to another hospital. Plus, there's no guarantee that he'll be able to make a smooth sailing career after leaving one of the best hospitals in the nation, according to the manhwa, even if he is really successful with an amazing reputation, because the Chairman might still interfere with his life thanks to his ridiculously overinflated pride.
That, and it's not like Sangmin will let him go that easily either, with his twisted sense of competitiveness, I mean, he did interfere with his results to make him go into the surgery department instead of dermatology ┐(￣ヘ￣)┌
Why is it that it has to be like this? He's an intelligent doctor and wise but why he can't just transfer to another hospital? Would it really matter to be working in a very large and well known hospital for you to be recognize?