Because, after I've blathered on about my carbon this and brand new that, they would shortly no longer be mine. Also, there are a few nutters on internet forums who would happily turn a disagreement on something menial into a war of words and threats against person and property. Imagine what these loons would do if they had your name and could find out your home address or where you worked.
I used to post on a motorcycling forum under my own name and got into a disagreement with another bloke over something trivial. My girlfriend picked up a phone call at 3am one morning and was told, in no uncertain terms, what a c**t I am. This may be true but I had no other enemies at the time and he'd found my home number and was now talking to my other half. I didn't sleep for a while after that.