IPA: /ˌæn.tiˈræʃ.ən.əl/
KK: /æntiˈræʃənl/
Not based on reason or logical thinking; opposing rational thought.
His antirational beliefs often led to conflicts with those who valued logic.
Antirational is formed from "anti-" (meaning against) and "rational" (from Latin "rationalis", meaning reasonable or logical). The word describes a stance or belief that is against reason or logic.
Think of being 'against' ('anti-') what is 'reasonable' or 'logical' ('rational'). This helps you remember that 'antirational' refers to something that opposes reason.