A lot of what is thought about people with Autism Spectrum is that they are rather insensitive people who are unable to empathize.
I may have said something about empathy before, but I'm going to do it again. This idea that autistic people can't be empathetic is just wrong! Have any of these "experts" even asked an autistic person how they feel about something? (Which is another topic for another time...)
In my experience, I usually know when society expects me to be empathetic, but during those situations I have NO CLUE what I should do. I usually end up doing one of two things: First, I become rather practical. If something needs to be done, I will do it. If there is some kind of tidbit of information I can give you, I will find it and give it to you. I want to help you solve the problem or feel better. I usually feel a sense of urgency about it too, as if the problem can't just wait for time to pass, but I have to fix it for you right now. There is something we can do about this anxiety I am feeling over what you are feeling, and I know how to find it and here's something to do. This is the insensitive side.
Second, I become disabled, mute, and avoiding. I usually want to but I can't say anything, do anything or sometimes even be in your presence.
Neither of these responses are socially appropriate. But what I have come to realize, is that the fact that I am not comfortable dealing with the emotional aspects of a situation doesn't mean that I'm not useful! In fact, if it weren't for people like me, how would things get done? Of course I've already mentioned my ability to find and share resources or info to possibly help. However, I'm also good at details. Give me a job! Let me help arrange something, or plan something. That way, I feel useful, I feel as if I am doing something for you during a time where I feel rather anxious about not being sensitive or empathetic enough.
So remember that the next time someone you know isn't acting sensitive or empathetic enough. There are likely thousands to millions of undiagnosed ASD's out there. Just give them a task, ask them to help you with something specific. It's worth a shot!