For the same reason you don't post your email, phone number, address, full name or social security number.
Sorry, that doesn't make any sense to me. You'll have to explain it to me better than that.
People don't post their email because spam-bots can pick it out and send all kinds of crap to your email address. Posting your license plate online is not going to fill your email with porn. Not the same reason.
People don't post their phone number because they don't want people to call them (I can only assume). Posting your license plate is not going to cause people to call you. Not the same reason.
People don't post their address because they don't want people to know where they live (could there be any other reason?). Posting your license plate will not tell people where you live (unless you happen to work at the DMV, but then they can tell where you live anyway...). Not the same reason.
I don't know why people have a problem posting their name.
Does anyone have a problem posting their name? Let's see if I do... Braden Kemp. Huh, nope. I don't get this one, but again license plate does not equal name, so not the same reason.
People don't post their SSN because it's a private piece of information that can be used for identity theft. Nobody can steal your identity by reading your license plate. Not the same reason.
Again, I'm sure there is a good reason, but I can't figure out what it is. Or is it just paranoia?