Why are titans killing humans?
Ok can't ask this question without expecting spoilers. 

Per Armored/Sentient titans attacking in the show, it was revealed why they're currently attacking (in the manga). Which is basically to get back the controller from Eren/Historia.

As for why the war is even happening and what causes non-sentient Titans to attack, that has not yet been revealed.  

**Side note a predominant current theory: It was mentioned the controller used to belong to armored titan's side of the war.  If that is true, non-sentient titans attacking humans on sight maybe a command from previous controllers instead of biological need. Also augmented by instances where titans ignored humans and attacked other titans.