Probably the logic of the ruling party: this president is not great, but if we impeach him now there will be elections and a new president will be elected, this time one from the opposition party. Competent president working for the other party might be considered worse than an incompetent and corrupt one.
I am sure they would vote for impeachment if they had real chances of winning the presidential elections.
Disclaimer: I know nothing about Korean politics, except some recent headlines.
Because its more complicated than him just being a bad guy.
He did a stupid, very bad move, but it was because the CCP-infected, anti-Japan opposition passed a budget that forced his hand, it would have apparently cut all government funding by a ridiculous degree.