If the details in the story are true, no I don't think he should lose his job.
He has been tormented for a year and a half.
He was hit in the face twice by these boys.
One of them spat at him.
Spitting at someone deliberately is classed as assault.
So if this is correct, they had targeted him for months and assaulted him three times that day before he pushed the boy.
I wouldn't be happy if this were my child who was pushed, but I'd be far less happy to find out my child had been tormenting a man for so long, thrown things in his face and then spat at him.
We live opposite a school whose pupils are aged eleven and over. We had a lot of problems with them throwing snowballs at windows and cars this winter.
Some of them made a point of targeting an elderly neighbour who is in poor health and this culminated with his window being smashed. He spent some of the coldest days of the year with a board over his window because he couldn't afford to replace the whole window and the glazier said the wood wasn't in good enough condition to replace just one pane.
It could have killed him, living like that, and I doubt the kids who broke the window thought about that or cared.
I don't have much sympathy for the boy this teacher pushed.