Hopefully the next time you see a PHP developer headed for your inputs with some backslashes and extra quotes, you'll have a clear mental picture of a concerned-looking medieval physician headed for you with a nice, sharp corkscrew.
The nice thing about this metaphor is that in addition to being a more accurate description of what you're doing, it's also a great metaphor about the kind of people who think that this is a good idea, as well as the state of the practice of technology that they are familiar with.
";--\ndrop table users;--"
isn't dirt; it's an active evil, a demon. You want to get it out of your string by making a little hole near the ";" to let it out. You're trepanning the string.
The issue is that you want to let the bad thoughts out of the string.
The issue isn't that the strings are dirty, and you're removing the dirt. After all, turning "<" into "\<" hasn't removed the objectionable material, it's just transformed it. Made it dirtier, even.
Let's stop calling it "Sanitization".