Example: You post a pic of yourself on the internet. Someone who doesn't like you for whatever reason, or just a random sociopath, picks it up and opens a webpage pretending to be you spouting off hateful shit to troll you. This then makes its way back to people you know and you have to go to some trouble to explain to people that no, this is not you and you don't know this guy's problem. What if it goes to your boss? Do you think they'd be as understanding? What if they use it to sign emails loaded with criminal pictures? The law is notorious for dragging its ass on stuff like this so you won't have any quick, legal recourse to take of this problem.
Now, I'll admit, this is a very paranoid way of thought, and it won't happen to the majority of internet users posting their selfies on the internet. But this extreme hypothetical is supposed to illustrate the total loss of control of anything you leave on the internet. The moment someone can tie it to you through your face or a name, you're leaving yourself open for disaster with hardly any defense available to you. Nary a month goes by without a story about some poor sod who left a digital paper trail on the internet and it came back to bite them.
I'm not particularly proud of it, but I've used Facebook to do some checking up on people/old contacts without explicitly letting them know that I'm looking them up. Having a Facebook account also lets me see numerous other Facebook profiles and glean information from them as well. If I truly wanted to wreck havoc, it would be very easy for me to do so.
But I don't, because I'm not a sociopath and I'm lazy. So think about it this way, the safety of your information on the web depends almost exclusively on others not being lazy and not being assholes.
I think that's a very tenuous security and not one I want to rely on.
