There are several synonyms for the expression "puts tail between one's legs," which means to feel embarrassed or ashamed after failing or being proven wrong. One synonym is "hangs one's head in shame," which implies a visible show of embarrassment. Another similar phrase is "eats humble pie," meaning to apologize and admit one's mistake. "Backs down" or "retreats" also convey the idea of admitting defeat or giving up in an argument or disagreement. "Crawls away" or "slinks off" suggest a sense of cowardice or timidity. All of these phrases convey a sense of humility in the face of failure or defeat.