I completely understand how that sort of thing of trying to parent or even just relate can be annoying. Personally if I pick up on something out of the ordinary about a person, I try to react in the most neutral manner possible. By not doing anything that says I’m trying to pretend I don’t see anything, but by also not having anything to say about what I am seeing. That being said, I think you made one slight error that opened up the pathway for the girl telling you about her experiences; and that was simply saying that you have a stutter. Objectively if you don’t want anyone’s input on something then you would just avoid bringing the matter to surface in anyway to begin with. Not saying anything in the first place would have been fine too. And while there’s nothing wrong with saying “I have a stutter” it is a bit farfetched to expect that all people would know to react without any response. While it’s true it could be annoying it’s also understandable that it seems like a natural response to most people so they do it.