The phrase "having at it" generally connotes a sense of passionate engagement, whether in conversation, physical activity, or conflict. Antonyms for this phrase would include terms like disengaged, indifferent, or apathetic. Instead of "having at it," one might metaphorically describe someone as "turning a blind eye," "tuning out," or "checking out." These terms suggest a lack of interest, attention, or energy. Antonyms for "having at it" thus convey the opposite sense of vigorous engagement and commitment, indicating a disinterest or disengagement with the situation at hand.