How can a male schoolteacher convince parents that he loves children, but not the wrong way?

probably by your actions

That's the unfortunate part of sexism of our society. The idea that the only way a man can love children is sexual.

He doesn't.  He should teach and mind his own business.  I suspect your teaching career in Korea is about to end.

He doesn't need to - just do his job.to the best of his ability. That will probably convince them anyway.