What most people mean when they say "antisocial". The word "asocial" is composed of the word social and the prefix "a-", meaning "not" or "to the contrary of," thus literally meaning something which is not or chooses not to be social or engage in social activity except when forced to.

To be anti-social, on the other hand, means to act strongly against the institutions of society; stealing mail, blowing up schools, sabotaging bridges and protesting prisons.