The phrase "cross swords" can be replaced with several synonyms that convey a similar meaning. The most suitable synonyms for this term are "argue," "dispute," "quarrel," "duel," and "clash." The term "argue" depicts a verbal disagreement, while "dispute" indicates an ongoing argument or disagreement between two parties. "Quarrel" typifies a heated disagreement, whereas "duel" represents a formal battle or confrontation. Lastly, "clash" denotes a confrontational meeting of two different opinions or ideologies. Each of these synonyms give a verbal nod or depiction of a clash of ideas, opinions, or belief systems.