Since I started being Anonymous, I realized how much better it is than posting with your name.
First of all, I must make it clear I'm not like those Anonymous users who misuse the anonymous function in order to troll or insult others. I'm strongly against it.
Anyway, my reasons are:
1) Posting Anonymous Will Make You Avoid Haters From Your Posts
If someone posts with his name and leaves anonymous option open (in order to let good anonymous users in), then there's a good possibility he/she might draw his/her haters to start bashing him/her. (Note: Those are the bad anonymous users.)
Posting anonymously will generally save you from that.
2) Your Activity Will Be Hidden
So you don't have to worry. You can respond to someone's comment whenever you want. You can take your time, without having him thinking:
"Why isn't he/she doesn't responding to my comment? He/she's online..."
3) You Can Ask Questions You Wouldn't Dare Asking With Your Name
Obvious, isn't it? And of course, I don't mean creepy ones.
4) When You Post To Someone Else's Opinion You Can Share Personal Experiences Easier
See #3. You can post a more accurate opinion that way.
5) Less PMs
Especially if you are popular and have a "Guru" or a "Master" badge. Many people might start taking you for granted. You will receive tons of PMs from various users asking you, "Could you please answer this/that?" After some point it becomes tiring.
6) People Will Focus On What You Said, Not Who Said It
Someone's "name" might affect his/her opinion to some degree, especially if he/she's one of the popular users here. When you are anonymous, your opinion becomes more neutral.
7) If You Have A Debate With a Hot-Blooded User, You Can Avoid Being Blocked
Some users tend to block someone else after just one disagreement without even letting you explain first. But being anonymous, they cannot do that, so there's a better chance to put them back into their places.