The phrase "crosses swords" typically refers to a situation where two people engage in a heated argument or conflict. However, there are several synonyms that can be used to convey a similar meaning. These include "clash," "dispute," "quarrel," "tussle," "bicker," "wrangle," "duel," and "spat." Each of these words has its own nuances and connotations, but all convey a sense of two opposing forces coming into conflict. It is important to choose the right synonym depending on the context and tone of the situation being described.