"Freedom of choice" isn't any kind of explanation, because the question is why do people choose not to post profiles.

I suspect it is as Carol C suggested, to do with a feeling that it's tooting your horn, which I don't think is necessarily so, but it can feel like that.

However something that a lot more people do is post a photo - but a whole lot more don't, and I think that's a shame, because it's fun to have a ganders at someone you are involved with in a discussion, or an argument.