It's a win-win situation for the witch/wizard/gypsy that cursed them. The witch doesn't like all of these monsters roaming around, and wants to thin down their numbers. The witch also doesn't like some poor sod for whatever reason, and wants to be vengeful against that specific person.
So, they place a curse that the person must eat a monster's heart/ bathe in a monster's blood once a week, or else suffer unimaginable pain. The person is doomed to a life of torment constantly hunting monsters, and the witch is cackling. There's nothing of value lost to the witch; only two inconveniences matched against each other.
The curse could be like an addiction; the victim becomes an addict, and the only way to get a fix is to kill a monster. The witch wants to get the best possible use out of her power; fewer monsters and fewer enemies.
Alternatively, you could easily replace 'witch' with 'government', 'military', 'church' or 'cult'. Perhaps the curse is a punishment used to run them of prisoners or undesirables. Instead of a hangman, they sentence people to death by monster hunting - a brutal form of community service, perhaps.
The reason why might be extremely petty indeed. It could be as much about getting rid of the person as is about getting rid of the monsters.
Alternatively, you have an effective means of turning a person into your slave. It is the ultimate torture/control. Any evil tyrant would spam the hell out of the ability and use it as much as possible.