Personally, I have a problem with it simply because I believe that if you have something to say, you say it as yourself. One should be willing to stand behind one's opinions.
My biggest problem with anonymity is that I will often see what I consider to be bullying, pressuring, or down right bad advice given out under the guise of anonymity. If you've got something to say to someone that is contrary, that's fine. The other stuff, I see no place for it. I feel anonymity in opinions fosters that culture. And if you're going to disrespect someone anonymously... I'll keep it civil.
I can understand why those would feel the need to ask some of the questions that are asked on here anonymously. Sometimes that's the only way that they can reach out. If you're going to offer your opinion, offer your advice, do so with your reputation and name behind you.