Bem, Sr. Bones e Ms Daunted's are fine meta-answers, if that's what you were looking for. Pretty sure you wanted the in-universe explanation.
He had no choice in the matter. A bad job market
From the beginning of S01E01:
— You're stalling.
— I'm not stalling. I'm not goin'.
— Ugh. Again? Honey, just be happy that you've been assigned anywhere. A lotta new teachers can't find jobs at all.
— Julie, James Buchanan is not anywheya. It's in Bensonhurst, which is in Brooklyn, which is where I spent four degenerate years as a student. Y'know how rough that is? The gangs theyah don' use guns. They insert the bullets manually.
and karma forced him into it.
The principal hadn't changed in the ten years he'd been out (presumably trying and failing at other gigs before settling on teaching) and still remembered and blamed him for a riot in the cafeteria. He took the opportunity to foist off his troublemakers on the new teacher he didn't like anyway.
— You haven't changed a bit, Kottah. You still have streetmouth.
— I have a degree in teaching, Mr Woodman. That's why we're here.
— You wanna teach? Alright, teach. I'm giving you back your own. The special-guidance remedial academics group.
— You're giving me the sweathogs??
— To you whose class launched that revolting name, they're "sweathogs". To me, they're... "remedial... sweathogs."
— Mr Woodman, d'y'really thin—
— Mr Kottah, you'll find that first aid is still in Room 118.
Of course, later, it all turns out to have been for the best.
— Oh no, please no.
— Hiiii.
— Kottah, like a prayer that was answered, you quit. You said up my nose with a rubbah hose.
— Remove the hose, Mr Woodman. I'm back! You want me out, you gotta fire me.
— I don't want trouble with the Board of Education. Y'know how I hate trouble with the Board of Education.
— I guess you're stuck with me, then, huh?