This can be a range of things, honestly.
I'll be quite honest with you, as someone with ASD, I do deeply care for my friends. But sometimes, I have a hard time relating to their negative emotions when they talk to me about what's gnawing at them. Don't get me wrong, I'm happy to listen when they want to confide in me. However, my natural inclination is to have an almost apathetic outward expression to when they tell me about the things that are bothering them.
So, I have to actually consciously play up my body language when they talk to me. Not in an over-the-top way, but more than I'm normally inclined to do. This is something I've gotten fairly good at with considerable practice.
So it's not that I lack empathy, because I do care that they feel bad, and I do want to listen. But the emotional response that they probably need is not something I'm actually capable of.
So it could be a sign of ASD? There are other types of psychological possibilities, too. You could always talk to a psychologist.