People are attached to images, especially the ones they use to represent themselves online. Even if it’s not a photo of themselves, it will usually mean something to them and can be unique on a pixel-level.
With services like Gravatar it’s easier to track someone by their avatar. Grab a copy of their avatar and paste it into reverse image search engines and you could find where that image has been used across the net. You could find the email addresses and accounts associated with that individual. You could build a map of their haunts online.
Your avatar is like a fingerprint. It allows you to be tracked almost as much as an email address. So take care when creating yours.