Antonyms for the phrase "taking the measure of" would be avoiding, neglecting, ignoring, overlooking, or disregarding. When someone takes the measure of something, they are assessing, evaluating, or getting a sense of it. On the contrary, when someone avoids or neglects something, they are not acknowledging or paying attention to it. Ignoring or overlooking something means not considering it as important or significant. Disregarding something means treating it with little regard or not taking it seriously. All of these antonyms suggest a lack of effort to understand or acknowledge something, in contrast to taking the measure of it, which requires careful consideration and attention.