I'm a vampire hunter. It's an inherited trait that was given to us by a vampire--so we each possess varying degrees of vampire DNA depending on our skill level.
[Not a lie at all. Even if he wasn't a vampire, Zero would probably still feel like one to other hunters to a small degree because of how strong he is. Kaien Kurosu, the former hunter that took Zero in after his attack, often trips up Zero's own senses which is saying something.]
The more powerful the hunter the more DNA they possess.