You're not doing anything wrong. There's a glitch in the system and for some reason we can't log out of the sister forums of BYC. You can log out of BYC! I know Rob is working on it.
I was never able to log out of BYC for the longest time. I have BYC and the sister sites on my favorites so I go to them from there, and I'm automatically signed in. I found out I had to go to google to find BYC from there to be able to log out.
Good to know they're working on it and its just a glitch.