Why the right to be forgotten exists in general: Let's say there was a widely publicised murder in your neighborhood. You get picked up by the police, your mugshot and name get plastered all over the newspapers. It's a mistake. They catch the real perp a few days later and you go free. Now every time someone searches your name they are greeted with your mugshot. You don't get jobs, you don't get to rent an apartment and so on. It's not fair, it doesn't serve society in any way, shape, or form. You should be able to get that information removed.

The same goes, of course, for any drunken party pictures and the likes, which should have no bearing on your life decades later.