There are many reasons why someone might use a pronoun other than she or he. The people who you expect might use a gender-neutral pronoun are not the only ones who do, and may be quite happy with he or she.
Most of the time, users make this choice because there is something about she or he which makes us uncomfortable. This often has a lot to do with gender, and many users have a gender identity or expression which differs from male/masculine OR female/feminine. Once again, however, this is not universal. Some make this choice for political reasons, or to make space for gender-neutral pronouns. However, the vast majority of people whose pronouns are gender-neutral are nonbinary, whether using that term or another one that is kind of like it. I go into this in depth in my book.
Using a gender-neutral pronoun like singular they can be a way to signal to others that a user does not want to be automatically grouped along with people who use she or he – usually women/girls/ladies or men/boys/gentlemen – for activities or invitations, etc. It can be a request that one’s preferences or habits or dis/likes or comfort not be assumed based on one’s (perceived) assigned sex. It can also be a way of making one’s felt gender apparent in everyday life by bringing it into immediate language.
So, using singular they is about comfort and communication. It can also be about many other things, and if you have a differing opinion or experience please share either in a comments section or on TIMP’s Tumblr.