The phrase "batted eyes at" typically means to flirt with someone, often through the use of coy or suggestive gestures. However, there are several antonyms for this phrase that convey the opposite meaning. For example, one might "scowl" at someone to communicate disapproval or disinterest, or "turn away" to indicate a lack of attraction. Similarly, if someone is perceived as being too forward or aggressive, one might "ignore" or "reject" their advances. Ultimately, the meaning of any given interaction depends on the specific nonverbal cues and language used, as well as the context and cultural norms within which it occurs.