Insists on is a phrase that implies a strong determination or insistence on a particular point or action. Synonyms for this phrase include persist, demand, press for, urge, and push for. Other synonyms that convey a similar sentiment might include enforce, impose, or compel. The use of synonyms can add depth and variety to writing by avoiding repetition and overuse of one particular phrase. Additionally, by using diverse synonyms, writers can modify their tone to be more persuasive or assertive, depending on the intended effect of their message.