The phrase "building fire under" typically means to motivate or inspire someone to take action. Antonyms for this phrase could include "discouraging," "dampening," "suppressing," "restraining," or "dissuading." These words all imply the opposite of building up motivation or excitement and instead suggest holding back or limiting someone's drive. It's important to consider the connotations of these antonyms when using them in context, as they may not always be appropriate or accurate. However, understanding the opposite meanings of "building fire under" can help deepen our understanding of how motivation and inspiration work in different situations.