Turning one's head could indicate admiration, surprise or curiosity. However, an antonym for this phrase could be "ignoring" or "disregarding." When someone disregards another's presence or actions, they intentionally avoid turning their head or acknowledging their existence. Another antonym could be "disinterested." This implies that the person is indifferent towards the situation or the individual, and hence there is no need to turn their head towards them. Lastly, "bored" could be another antonym for "turning one's head," indicating a lack of interest or stimulation in what's happening, resulting in not bothering to turn one's head to pay attention.