Thematically, I think the idea is that it's a life-leeching bite so it's not just a dog taking a bite out of you. Teeth chomp and restore his own life force through what is assumed to be magic.
Balance wise, he's an autoing champion. Not only is armor equally effective versus autoing champs, it also has specific items tailored to that type of attacking. Ninja Tabi, Thornmail, Frozen Heart, Randuin's omen all have extra damage reduction effects on autoattack-AD as opposed to spell damage AD.
I don't necessarily agree with it on Warwick specifically, but auto-champions tend to have some way to do a bit of extra damage past their simple rate of DPS. Tryndamere has 5 seconds to deal extra damage as well as free crit, Master Yi gets double strike, steroids and true damage, vayne the same, Olaf gets increased attack speed that scales in battle and steroids, xin zhao has guaranteed crits and armor reduction through autos (Sort of) and guaranteed heals with autos, etc. Point is, auto-based champions typically are given ways to deal extra damage due to the fact that their are more tank stats available to counter their damage specifically.