Dante doesn't mind killing humans, he shot Sanctus before "the ascension ceremony", the anime still contradict a few things too, like Trish being Dante's partner...etc, so don't take every quote in the anime so seriously. the anime is canon, but if 2 sources contradict each other, you have to take the more official source.
Lexy, Dante didn't hate demons, he gets satisfaction from killing demons that's all, in DMC1, Griffon kept going after him, & when he got wounded, he tried to talk him out of the fight, & Mundus ****ed him off when he killed him "His heinous ways make me sick, killing even his own, like they were nothing". in DMC4 they tried to make Dante look like he cared, like after he defeats Berial "you can stay & die, or you can walk your ugly ass back through that gate", they wanted to make him as sarcastic as possible, it doesn't work this way for Dante. I almost haven't noticed this characteristic that carried over from the original.
I don't think of Dante as a hero, that was just figure of speech, I see him as a liaison of the humans & demons, if a human wants another demon's power or something like that, he'll stop him, if a demon wants to rule the human world or destroy it, he'll stop him.