The phrase "is big about" means being passionate, enthusiastic, and intensely committed to something. The antonyms of this phrase will be words that convey disinterest, lack of commitment, and indifference. Words such as indifferent, apathetic, uncommitted, dispassionate, unconcerned, and uninvolved can be used to describe someone who is not "big about" something. These antonyms suggest a general lack of emotional investment, engagement, and interest, as opposed to the fervour and dedication that the original phrase implies. Therefore, it's important to choose the right words that accurately reflect the level of commitment towards a particular matter.