IPA: //ˌæn.tiˈsoʊ.ʃə.lɪst//
KK: /ˈæntiˈsoʊʃəlɪst/
A person who is against or does not support socialism, which is a political and economic system where the means of production are owned and controlled by the community or the state.
The antisocialist argued that socialism limits individual freedoms and economic growth.
Antisocialist is formed from "anti-" (meaning against) and "socialist" (from "social" derived from Latin "socialis", meaning pertaining to society, and the suffix "-ist" meaning a person who practices or advocates). The word describes a person who is against socialism or socialistic principles.
Think of someone who is 'against' ('anti-') the ideas of 'society' ('social') — that's what antisocialist means.