Well, they’re all good enough reasons, although obvious.

Can I offer a twist:

The story would require 2 villains.

Villain 1 coerces the hero into seeking out and killing Villain 2. This could be blackmail, or perhaps he has the hero’s family as collateral.

The hero then has to find his target, kill them and return. If he doesn’t return in X days, the family starts being killed.

Obviously Villain 2 may not be a “Villain” at all, but that’s what the hero has been told. So he thinks he’s doing the right thing.

Ultimately the hero will have to make a choice. Save his family and commit a gruesome murder, or do the right thing and see his loved ones suffer.