Well, it might be in your interest to know if someone plagiarizes you. I don't know anything about Turnitin, though I doubt they notify the original copyright holder?
If you provide copies of your work for free on the internet, this is why they get to keep one, just as everyone else? They are probably not allowed to distribute it, though?
I don't think they're talking about posting your work for free on the internet, they mean when you submit an assignment for a class turnitin stores your assignment so they can check future submissions against yours. In this case, you haven't (necessarily) shared it anywhere public, all you did was submit it to your teacher, and now turnitin gets a copy forever.
