
Painter also secretly wants to get his ass f*cked, lets be real here.
I was thinking that maybe the teacher is a "sodomite" himself but he thinks that porn is unrefined. Very unlikely but it would be fun.
OR, he paints gay porn as well and Na-kym is his artistic rival, he'd naturally want to get him out of the way ╮( ̄▽ ̄)╭
Maybe he's just testing the waters with Yoon?

Teacher wants power i.e. government position. He doesn't care for Na-Kyum at all and is only acting friendly toward him because Na-Kyum "spoke highly of him" (Seungho is using the teacher as leverage to get Na-Kyum to paint). However!!! Seungho does not know that Na-Kyum doesn't paint anymore because of the teacher. I think once Seungho finds out that's the reason why, he'll get rid of him. Overall both are abusing Na-Kyum's feelings for the teacher
But I reread this and realized Shady Teacher did not tell the real truth to Yoon.
He told Yoon "I once caught (painter) drawing something bizarre and vulgar for which I scolded him severely". However, in ch 10 he tells (Painter) "To think you who once sold paintings of sodomy..."
So he knew all along that the Painter had been selling erotica under a pseudonym, but left that out with Yoon (which I get). Shady Teacher knew Yoon is a sodomite and the Painter draws Sodomy. Yet he played dumb with Yoon and accepted his offer of help. However, he told the Painter, "I hope you don't still draw that stuff".
Did Yoon make up the Teacher wanting to visit Painter or did he invite him there and only tell the Painter that? It looks more like the Teacher did want to see the Painter and Yoon allowed it because that worked to his favor.
Shady Teacher seems to have a hidden an agenda. If he was hell-bent on the government post he'd be supporting the Painter. He isn't. I think he's after something else.