This is interesting because as I thought through various scenarios, I realized that I have some distinct different reactions to different situations.
A lot of time, when people who know DD realize that I'm her parent, I get "oh, she's so smart / smartest one in class" or turning to friend or spouse and saying "she's the one I was telling you about who's so smart" or similar. This doesn't really bug me and I usually just take it in stride. After all, she IS smart and it's not really my doing or my fault. In this context, it really is similar to saying "with the red hair" or "the really tall little girl."
On the other hand, I react very differently when people do this sort of thing in group introductions. It's just feels so announcement-like. I'm a private person and I really hate when people do this with any kind of personal information. For example, I went to a dinner at a friend's house with a bunch of other women and she introduced everyone to everyone else by going around the room and telling everyone stuff about everyone's life. All the details were nice and even complimentary -- my friend meant no harm -- but I nearly died on the spot hearing facts about myself broadcast to a room of near-strangers. I think "brilliant daughter" got a mention, but so did a bunch of other things that, while I don't necessarily keep secret, I don't need everyone hearing about from a third person. It just comes across as "let me tell you interesting things about all the interesting people I know."
Gah, sorry for the rant. But I agree with the original poster. I think this sort of introduction should be more like: "This is George everyone, his son is Daniel -- he and Mary met at soccer camp last summer." Then everyone can decide on their own how much to share about their lives and children.
