Antonyms for the phrase "had a bearing on" can range from terms that indicate a lack of effect or influence, to words that imply that something occurred independently. For instance, antonyms could include phrases like "was irrelevant to," "had no connection to," "was inconsequential to," "was unrelated to," and "did not impact." Additionally, synonyms that suggest an outcome arrived at due to factors outside of one's control, such as "was predetermined," "was fated," and "was inevitable," could also be considered as antonyms. The range of corresponding terms to "had a bearing on" is broad and can vary widely based on the context in which the phrase is used.