Why won't my CORRECT Apple ID password work on iMac but it works on iCloud?

I am trying to do the new iPhone mirroring thing (but the same thing happens when I try to do other stuff...). When I try to use my Apple ID on my imac (latest software installed), it doesn't recognise the Apple ID password I know is correct. Instead, I have to say I want to log in using another email, whereupon I type in the Apple ID and it does work. It's definitely that both are asking me to enter the password for the same email address. I can easily access icloud by doing this and the same on my phone but it's annoying to have to do it this way - especially as I'd like to use the new iPhone mirroring and seem to only be able to do it if my mac logs into the Apple ID NOT via the cloud website.

Any wise words as I cannot be the only person? I've checked through the help articles and they are all 'change your password' or 'make sure you don't type in uppercase' - checked and not relevant.