Sociopaths don't understand sarcasm

I think this conversation with a friend is interesting because it illustrates how completely oblivious I am to sarcasm. I frequently get accused of blaming every trait of mine on being a sociopath, but I think this one is actually true because aspies and other empathy-challenged individuals also supposedly struggle with understanding sarcasm. Although I don't understand how one's ability to feel for another would lead to being able to correctly interpret hidden meanings behind words. Uh... actually, after having just typed that out, it does seem to make some sense.

Friend: I just read on facebook that [a mutual friend] is a sociopath.
M.E.: What?! Really?!
Friend: Or actually, he replied this way to a question regarding his most embarrassing moment: "None, because I'm a sociopath."
M.E.: Whoa! That's crazy. I never would guessed.
Friend: Ok, sorry I thought you would realize that he was kidding and would laugh at it. I keep forgetting that you don't understand sarcasm.
M.E.: ? How do you know he was kidding?
Friend: Well, think about it this way: only neuro-typical people would say they are a sociopath. Sociopaths wouldn't want to out themselves and they wouldn't risk even joking about it for fear of accidentally outing themselves.
M.E.: Hmm, well, you got my hopes up for nothing then.