The term 'speak irrationally' can be broken down into two crossword solutions: RAVE and RANT. To 'RAVE' is to speak or write with great enthusiasm, often in an exaggerated manner. It is usually used to describe someone who is expressing their admiration for something. To 'RANT' is to speak or write in an angry or violent manner, often without any logical reasoning. It is usually used to describe someone who is expressing their anger or frustration about something. Both of these terms are used to describe someone speaking irrationally.