I think it's important to differentiate between asocial behaviour and anti social behaviour.
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Antisocial Personality Disorder is a condition characterized by persistent disregard for, and violation of, the rights of others that begins in childhood or early adolescence and continues into adulthood. Deceit and manipulation are central features of this disorder. For this diagnosis to be given, the individual must be at least 18, and must have had some symptoms of Conduct Disorder (i.e., delinquency) before age 15. This disorder is only diagnosed when these behaviors become persistent and very disabling or distressing.
Possible disorders which could be associated with social problems
1) Borderline PD
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People with BPD often have highly unstable patterns of social relationships. While they can develop intense but stormy attachments, their attitudes towards family, friends, and loved ones may suddenly shift from idealization (great admiration and love) to devaluation (intense anger and dislike). Thus, they may form an immediate attachment and idealize the other person, but when a slight separation or conflict occurs, they switch unexpectedly to the other extreme and angrily accuse the other person of not caring for them at all. Even with family members, individuals with BPD are highly sensitive to rejection, reacting with anger and distress to such mild separations as a vacation, a business trip, or a sudden change in plans. These fears of abandonment seem to be related to difficulties feeling emotionally connected to important persons when they are physically absent, leaving the individual with BPD feeling lost and perhaps worthless. Suicide threats and attempts may occur along with anger at perceived abandonment and disappointments.
2) Avoidant PD and Social Phobia
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Anxious (Avoidant) Personality Disorder is a condition characterized by extreme shyness, feelings of inadequacy, and sensitivity to rejection. These individuals feel inferior to others. This disorder is only diagnosed when these behaviors become persistent and very disabling or distressing. This diagnosis should be used with great caution in children and adolescents for whom shy and avoidant behavior may be appropriate (e.g., new immigrants).
3) Schizotypal PD
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Schizotypal personality disorder is a serious condition in which a person usually has few to no intimate relationships. These people tend to turn inward rather than interact with others, and experience extreme anxiety in social situations.
4) Schizoid PD
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Schizoid personality disorder is a condition in which people avoid social activities and consistently shy away from interaction with others. People with the disorder are generally loners with a profound inability to connect with others and form personal relationships.
As far as I know that is it, although any type of emotional problems (anxiety, depression etc) could also be associated with it. Hope this helps.