I recently had an issue with changing the pimary email address for my Apple ID. I'm talking about the one listed here:

If you try to change your Apple ID, chances are you'll run into some issues, the most severe being that you can't re-sign into iCloud on your Mac. OS X doesn't automatically update your Apple ID to the new one. Instead, you have to go to Settings -> iCloud, sign out of your old Apple ID, and then sign in with your new Apple ID.
The trouble is, you might experience this error:
Your iCloud account couldn't be removed at this time. Turn off all iCloud services and try again.

Thanks, Apple. That's what I was trying to do.
The Problem
If you notice in the picture above, Keychain is not disabled. Every other iCloud service I could disable, but despite whether I tried to delete Keychain or keep Keychain, it would not stay disabled!
Why?! Why can't I turn off Keychain?!
What Worked
I came across a viable solution in the Apple forums, which I'll explain here.
To disable Keychain under your current user, you're going to have to reactivate Keychain under another user account. This can be accomplished on the same or different machine. If you only have one Mac, like I do, complete the following steps. If you have two machines, just infer the differences.
I solved my issue the long way, but I think the shorter way might work, too. The difference lies in whether you revert your Apple ID to the old one at the beginning. Your call!
The Long Way (I Know Works)
- Revert your Apple ID to the old email address here.
- On your Mac, in Settings -> iCloud, log back in to your iCloud account.
- Click on the Options button next to Keychain and make sure that you have set up a Security Code and Verification Number.
- Do everything in the Short Way. Ha!
The Short Way (Untested)
- Create a new user account on your computer.
- Switch to that user.
- Go to Settings -> iCloud and sign in to your account.
- Enable Keychain and authorize it either way, as long as you're able.
- Switch back to your regular user account.
- You should now be able to disable Keychain and sign out from iCloud on your Mac. Do so.
- If you started with the Long Way, go online and change your Apple ID to the new one you wanted.
- Log into iCloud with your new Apple ID on your Mac.
If you were successful, you can go ahead and delete the temporary user account that you made.
If you were unsuccessful, double-check the directions. Or maybe your problem isn't with Keychain and a different solution below might do the trick.
Either way, let me know what you did and what worked/didn't work in the the comments or email me at matt at apatchofcode dot com.
What Didn't Work (For Me)
I tried a few other things, and while I can't be sure if they worked, I've listed them here so they might help someone else. I'm not going to list dangerous solutions like deleting things.