An important thing to note is that Logan is not human! Yes, he looks human but he isn't. He is a feral mutant. He is his own species.
My theory how the feral mutants were created is that they evolved from canines and mustelids rather than apes. So alongside the Neanderthals they were these beings and they carried the X-Gene and mated with the modern human thus creating the mutants that Logan's paternal side of the family descends from.
And Logan has a lot of animals qualities. He has claws, little fangs and is nocturnal. He hunts and has keen senses. Yes, he is civilized from living among humans but trigger him enough and he will growl at you.
And Wade accepts that. He accepts Logan for who and what he is, rather than tell him what he should and shouldn't be. (Unlike Kayla and Stryker cough cough) And Logan finally learns to love himself, something he hasn't done in all his lifetime