The phrase "backs down" refers to when someone retreats from an argument or situation. There are several synonyms for this phrase that can vary in intensity. For example, the phrase "concedes" implies that someone is admitting defeat, while "yields" implies that someone is giving in to someone else's demands. "Retreats" and "withdraws" both suggest that someone is physically backing away from a situation. "Capitulates" is a strong synonym that implies complete surrender, while "compromises" suggests a negotiation or agreement between two parties. Alternately, "retracts" suggests that someone is taking back what they originally said or did, while "surrenders" indicates giving up control or power.