There is a clear distinction between pride and boastfulness - even the most socially inept should be able to recognise that.
Boastfuness in both adults and children is not pleasant to be around, and while it may not affect our lives one jot, it does put us off wanting to be around those who do it.
My NCT groups occassionally circulate emails where we update each other on our little ones' achievements. However our babies are all just 12-14 months, so their achievements are purely developmental; not the result of a budding Einstein, or superior parenting skills. This doesn't seem to resonate with most of them, though.
I think the thing I most dislike (despise is a strong word, and I honestly don't think the OP meant it literally!) about boasting is the inherent assumption that the boaster's child is better than the boastee's.
The main thing that stops me from boasting (aside from not wanting to be totally sidelined as a complete and utter bore) is the belief that whatever I come out with will be spectacularly trumped and I'll be made to look completely foolish, though this doesn't stop many...
Oh, little Tarquin has negotiated peace in the Middle East? Well, Henrietta discovered a cure for AIDS 5 months ago!