I know this is a thread about a thread but it was really irritating me.
"I don't like precocious children", "I don't want to engage with somebody's precocious child". Being precocious isn't in itself a bad thing! It just means unusually talented for their age.
Replace the word with 'cocky' and I'd understand, but written like that it makes no more sense than saying "I don't like shy children". Well, it makes sense, but it isn't what the many, many posters meant.
Agree that the word precocious itself should not be construed as inherently pejorative. However the implication is that the children are both precocious and show-offs. I think that they two coincide so often that precociousness is now generally assumed to go hand in hand with showing off, so it's implied.
May also be linked in people's subconscious to the similar-sounding adjective "precious" which is of course negative when used to describe behaviour.