How can I completely de-authorise my account from iTunes (mac)?
Signing out of your account and deauthorizing a device are two different things.

Within iTunes you can actually sign in and out of multiple accounts. I don't mean simultaneously, just that you can sign into one and, if needed, sign out of that account and then sign in using another account.

Authorising a device basically tells the iTunes ecosystem that it's allowed to play your purchased music, videos etc and that's why there's a limit to how many devices can be authorised for any particular account. So, deauthorizing a computer/device is typically something you would do when you're going to sell it etc.

If you want to sign out of your old account in iTunes you should actually do that within iTunes. You may need to sign in again first and then sign out before signing in with your new account.