The phrase "being big on" refers to having a strong preference for or being passionate about something. It is often used to express enthusiasm towards certain activities, beliefs or values. However, there are several antonyms that can convey a different meaning. Words like 'indifferent', 'cold', 'aloof' and 'dispassionate' indicate a lack of interest or enthusiasm. Words like 'moderate', 'balanced', 'unbiased' and 'dispassionate' convey a sense of neutrality or objectivity. Additionally, antonyms like 'small', 'insignificant' and 'unimportant' detract from the idea of being important, significant or valuable. Therefore, it is essential to choose the right antonyms depending on the context and the intended meaning to avoid miscommunication.