I was thinking about this question of pity when someone opens up and although I can easily see a potential correlation, it is also foreign to me. It made me realize that some people discuss emotions in a more abstract way using moments of personal experience to demonstrate credibility or to just serve as an applied example of whatever social or emotional system is being discussed. When viewed with the following assumptions, pity just isn't a part of the process.
For example, if there was a discussion about growing up with alcoholic parents, and someone opened up about their experience, it wouldn't occur to me to pity them - or that they were seeking pity. It would establish information and their position in viewing that information. If they had learned from the experience and were able to look at it, define it, and create systems of thought making sense of it, then I would admire that and appreciate a type of expertise and strength they had developed. There are inexperienced, naive people online making big claims, so in discussions it helps if people approach things honestly and with openness to get a sense of where they are coming from. I suppose discussions could look for credibility in statistics and research, but if the focus is on personal impact, then it makes sense to explore it in that way.
Being on the receiving end of pity is not an enviable position, and I tend to doubt it is a common motivation. The assumption that emotional discussion correlates with pity assumes it also correlates with weakness. Most emotionally based discussions I perceive as being about how to be stronger - a person can't be strong if that hasn't been tested and placed at great risk (i.e. if they haven't been in a position of vulnerability). There isn't a way to know how strong a person is until you understand how they respond to vulnerability because that usually reduces a person to their core self pitted against obstacles. It's about seeing a person with all their advantages stripped away and seeing who they are and who they choose to become after that experience.