Don’t send me e-mail about this, because yes, your dictionary might say that the distinction between the two words is hazy at best, but shades of meaning are important, and anti- words mean active opposition while a- words mean absence. If you’re confused, use antisocial, which has a more inclusive meaning. Killing a dude isn’t asocial, but most dictionaries will let you get away with saying that pretending not to see that guy you know on the train is antisocial.