Note: This is a misfeature of Facebook, but consideration might be given by StackExchange to working around it.
If someone discusses a topic on Facebook that is covered by a Stackexchange question, I will cut and paste the URL into a comment.
Facebook, in its urge to provide visual clues, automatically looks for some image to include with the link to act as a preview.
In practice, the first image it finds is the avatar of the last person to edit the question. As much as I think we should acknowledge the fine work of the editors, this is not an appropriate image to go with the question.
I do not know the rules Facebook uses to select an image. I do not know if Facebook publish a mechanism for site-owners to provide an appropriate image. Facebook has published how to indicate the appropriate image.
It would be nice for the selected image to be the icon appropriate to the site, not a cartoon picture of a random user.