The problem is that more intellectual ability is better, so a parent of a normally developing child is always at risk of taking your intent to be presentation of your child as superior (which they are in a key respect, no way around it). Due to the gap, we may have to spend a little time and effort to be tactful to make sure someone understands that we're not trying to lord it over them.
I think that the reason people aren't so touchy about athletic prowess is that it's easy to rationalize away any differences without affecting one's feelings about one's child. Intelligence is seen as static by most people, whereas athletic prowess is always in large part the result of tremendous amounts of physical labor. Athletic prowess tends to be limited to the first 2-3 decades of life, and thus has a limited potential payoff, whereas high intelligence generally lasts until old age. Developing athletic ability takes a big time commitment and sometimes money commitment on the part of a parent (whereas the common conception of the gifted may not see it the same way even if true), and a parent might feel that their child could be a high athletic achiever too, except that they've made other choices, perhaps to focus on academics... no parent who wants their child to be successful would ever trade away intelligence for some other goal.
Parental intellectual competitiveness by proxy is understandable, because people want the best for their children, and the ones most focused on that often don't want to consider that their children are limited in any way. Children with naturally high abilities threaten those parents' conceptions about their children. This is a scenario that will be repeated forever, or until we are all gene-tuned cyborgs with incomparable abilities. In the meantime I think it's best to work on self- and other-perception in order to keep feathers as unruffled as possible, without making apologies for who we are.
