"Antisocial", in the mental health field, is not someone who is quiet and enjoys spending a lot of time alone or someone who doesn't socialize a lot. The word "antisocial" is shorthand for Antisocial Personality Disorder. An "antisocial" person is basically a sociopath. Someone who is antisocial has no regard for the rights of others. They live only for themselves and consider other people only as a means to get what they want. They will lie, steal, manipulate and maneuver to satisfy their needs. And they will do so with absolutely no remorse. They are smooth and glib and lie effortlessly. Their relationships are parasitic and they have a perverse inability to conform to societal norms.
I think the word people are looking for is "introvert" as in someone who avoids social interactions and prefers to be alone.
An introvert is; a person who shuns social events, a person characterized by concern primarily with his or her own thoughts and feelings, a person who turns inward for comfort and sustenance.
This raises another question. Many seem to believe that a desire to avoid social interactions and to spend a great deal of time alone is "abnormal". Introversion is not abnormal. It is simply another way of being. Some people are extroverts. Some people are introverts. Some people have dark eyes. Some people have light eyes. Both are normal. They are just differents "flavors" of a human characteristic. Some people are naturally more outgoing social butterflies. Some people are more intrigued by exploring the depths of their own minds. Extroverts are energized and revitalized by being around people. Introverts are energized and revitalized by thinking and reflecting. Some very famous people drew their ideas and ideals from quiet time spent alone; Albert Einstein, Steven Spielberg, Charles Darwin, Mahatma Gandhi and Henry David Thoreau.
An introvert is not someone who suffers from shyness (or the medicalized "Social Anxiety Disorder"). Introverts can be quite comfortable and adept in social situations. They prefer to be alone not because they are incompetent at being social, but because it drains their energy. Social events stimulate and energize extroverts, but drain introverts. At the end of a long day an extrovert will look for a party to kick back and enjoy themselves. An introvert will look for a quiet corner and a book. Both choices are healthy and normal - for that individual. People are different and they are nurtured by different things. Being different does not mean being mentally ill.