Mutual hostilities is a term used to describe a relationship between two parties that is marked by deep-seated enmity, ill will, and antagonism. The antonyms for this phrase are words that describe the opposite, which is a relationship characterized by goodwill, cooperation, and harmony. Some possible antonyms include amicability, friendliness, peace, reconciliation, and understanding. These words denote a state of mutual respect and agreement between two parties, and they indicate a willingness to work together in pursuit of common goals. In contrast to mutual hostilities, the antonyms suggest a desire for harmony and cooperation, rather than conflict and animosity.