I'm not very good at this, but I've suspected it could be about showing kindness/being fair in any other way than offering the same weight(?) in information.

I think the other posters have it right that being a good listener (including asking good questions) alone can support the whole conversation. With me the over-sharing has mostly happened when it's about me worrying about the other person feeling somewhat unfair if I don't talk about some personal stuff too.

I think with questions I worry mainly about me asking the person anything putting them in a place where they're forced to answer about something they don't want to. Maybe it helps to get better at this, asking a question and making sure the other person feels at ease not answering it....I'm lurking here to find out more.

Edit: missed a word