Reason the Boss punished Kim (never explained explicitly)
In the final showdown, Kim asks the Boss why he was treated so badly after "7 years of working for him like a dog." There's a pause, then another. And the Boss refrains from answering so Kim shoots and kills him.
I guess its obvious, but its interesting that they didnt explicitly reveal the reason.
My obvious guess is, Boss sees how Kim spares the girls life and lies about it. Boss knows Kim is attracted to girl and knows all things being equal that she would prefer Kim over himself. Boss doesn't for a moment think Kim is cheating on him with the girl. And that perhaps makes it even worse: because Kim /is/ honorable, he /has/ served him faithfully and honorably for 7 years. That, combined with his youth, does make him a better match for the girl than the boss. So he acts to destroy this "rival", by humbling him so much so that he is no longer a contender for the girl, or failing that, by killing him.