People with Asperger’s syndrome/HFA often have a different way of showing empathy than other people, so some can appear to lack empathy when they actually don’t. Also, if a person lacks empathy in one situation it does not necessarily mean that they cannot have empathy in a different situation, so don’t assume that they completely lack empathy.
People with Asperger’s syndrome/HFA can learn to become more empathetic or to show empathy in more typical ways.
It is easier to be empathetic when we can somehow relate to what the other person feels or what they are going through. Then we know what it feels like. It’s harder to be empathetic when we have no idea what the other person feels like, for example if we haven’t experienced anything similar ourselves or if the person is upset about something that would not upset us. The more experiences we have ourselves, the more we get to know what the same situations must feel like for others and that makes it easier to be empathetic. We can also learn by observation about how other people show empathy and then we can try to mimic that so that our empathy shows more clearly too.
Since people on the autism spectrum and neurotypicals (people who are not on the autism spectrum) are different in many ways, we don’t always experience feelings the same way. Sometimes we don’t understand why other people are upset or excited, because we wouldn’t be upset or excited about the same kinds of things, so it’s hard for us to be empathetic. Likewise, sometimes neurotypicals don’t understand why we are upset or excited, because they wouldn’t be upset or excited about the same things as us, so it’s hard for them to be empathetic towards us. Neurotypicals may have plenty of empathy towards each other, but in my experience they have little empathy towards those who are different, like autistic people, simply because they don’t always understand how we feel. It’s the same with us, we are more empathetic towards each other than towards neurotypicals, because we understand each other better than those who are different (neurotypical). It’s just more obvious with us because there are so many neurotypicals and so few autistic people in comparison, so you are more likely to notice lack of empathy on our part.
I have Asperger's syndrome myself.