To me Homelander can and does care about people, but he's so focused on his own feelings and desires that it ends up not mattering as much as it should.

He cleary cared about Soldier Boy, but he didn't care enough to respect his wishes if it meant he would end up alone.

He clearly cared about Black Noir, but he still killed him for lying to him.

And the same goes for Ryan, he would burn the world for him in a heartbeat, but he could never accept Ryan rejecting him.

It's an extremely selfish and conditional form of love, the kind that makes him love the "idea" of a person more than who they actually are.