I have a very poignant memory of the first time I heard a girl call a guy "cute." It was when I was about 11 years old. My friends and I were out in the playground during recess, and urgently needed to confirm a recent rumor that one of the girls in our class "liked" one of our friends. So of course we went as a group to confront her and her friends to investigate. I forget if the girl in question made the comment, or if it was one of her friends speaking on her behalf, but the salient response was that she thought our friend was "cute."
I was instantly repulsed by the word. I remember thinking it sounded condescending and inappropriate – or, as my sophisticated 11-year old mind phrased it, "like he was a little bunny or something." I remember immediately questioning her use of the word, and making it clear to her that I hated it. Seventeen years later, my opinions haven't changed much, although they have been dulled somewhat by the word's increasingly common use.
Anyway, that was a long way of saying that I think the primal instinct in a man is to dislike or even hate being called "cute," or more specifically, we hate what "cute" implies. Men want to be admired, not adored, and this adjective doesn't exactly reinforce a man's confidence in a woman's admiration. A woman calling a man "cute" is similar to a man calling a woman "nice," which sharply undercuts your understanding that he adores you, or could adore you - or at the very least, that he sees you as a woman who could be adored. It relegates you to the realm of "mildly attractive," in the same way that "cute" relegates a man to the realm of "noted but ignored." Granted, this is not always what a woman means, since "cute" has gradually come to carry more and more weight as a typical descriptor for "attractive." But it is ambiguous at best to men, and still does very little to connote admiration.
These kinds of compliments highlight his masculine strengths and your admiration of them, rather than downplay his physical attractiveness, which is about all you accomplish with "cute."