If you look up what genre We Need to Talk About Kevin is in, you'll find it under “psychological drama.” However, much like I’d consider Mulholland Drive a horror movie, even though it’s categorized as a “mystery film,” I’d say the same thing about Kevin, as it’s straight-up horror.
In fact, I actually think WNtTAK is one of the greatest horror movies of all time that pretty much nobody talks about. Sure, I know most people wouldn’t put it on a list of the best horror movies of all time, but that’s only because many people seem to overlook “realistic horror,” such as If I Had Legs I’d Kick You (which is another great “horror” movie).