The phrase "made heads or tails of" refers to the ability to understand something, often after it has been confusing or difficult to comprehend. Some antonyms for this phrase could include "perplexed," "bewildered," "mystified," "confused," "stumped," "befuddled," "puzzled," and "flummoxed." These words suggest a lack of clarity or comprehension, which is contrary to the notion of making heads or tails of something. Other antonyms could include "ignored," "neglected," "overlooked," "dismissed," and "disregarded," which imply a lack of interest or attention to a particular matter.