The antonyms for the phrase "meeting eyeball-to-eyeball" include avoiding eye contact, looking away, ignoring, and evading. When individuals are not comfortable being direct with someone or are avoiding a confrontation, they tend to steer clear of meeting eyeball-to-eyeball. This can be seen when individuals are dishonest, hiding something or are not ready to share their thoughts or opinions with others. In certain situations, people may choose to ignore eye contact because they are shy or lack confidence. Alternatively, evading eye contact could be a sign of deception, nervousness, or insecurity. Overall, there are several reasons why someone might seek to avoid meeting eyeball-to-eyeball.