The phrase "be neck and neck" refers to a highly competitive situation where two opponents are closely matched in terms of performance, often in a race. The antonyms for this phrase could be "fall behind," "lose ground," or "lag behind." These terms denote a situation where an opponent is not performing as well as the other and is not keeping up with pace. Another antonym could be "pull ahead," which suggests that one of the competitors has taken the lead and is no longer closely matched with the other. In short, antonyms for this phrase indicate a lack of progress, competitiveness, or close match.