The main meaning of 可愛くない is of course "not cute", but I think I've heard/seen the word in other contexts, too. Is it possible for 可愛くない to be a kind of insult, like "loser" maybe? Especially when it's used for boys?
可愛い has a wide variety of meanings, but in your case it probably means "adorable", "innocent", "docile" or "childlike". For example, if a 9-year-old boy refuses to help his mom after saying a sarcastic and argumentative remark about money, that can be 可愛くない.
I sometimes see it used in the sense of "mean" or "ungrateful":
You're not very nice.
I bought you donuts and you're not even thankful!