Try going to the iOS device and sign out of iCloud Keychain there, then see if the sign out sticks on the Mac.
The phone I mentioned is not an iOS device, not even a "smart" phone, and it has never been connected to iCloud. I used it as an e-mail address only. My MBP was connected to iCloud, but I managed to turn iCloud Keychain off on that device.
The MP just refuses, (has a exclamation mark and the message "waiting for approval from other device").
Tried iCloud.com, using Chromium, intending to access the advanced settings, but I could not get access. An error message popped up, "There was a problem .... " typical worthless error message - with "send a report to Apple" and "OK" buttons. um.... That is certainly not OK .....
Using Safari, I got access to the Settings page, but did not see how to sign out at all.
The original keychain access issue persists....