The antonyms of "are solicitous of" are words like indifferent, apathetic, unconcerned, uninterested, and neglectful. When someone is solicitous of something, they are showing great care and attention to it. On the other hand, someone who is indifferent or uninterested does not care about the thing in question. Neglectful implies a lack of attention or concern. The antonyms of "solicitous of" suggest a lack of concern, attention, or care, and a general disinterest in the matter at hand. It's important to be mindful of these antonyms so that we can accurately communicate our intentions and attitudes towards different things.