not login on my Mac iMessage

Messages – Can’t log in

Messages – Can’t log in 2

Messages - If you can‘t sign in to your iMessage account or FaceTime on your Mac

Message activation error

You can also try signing in on another device/computer. There have been a couple of posts where people's device/computer was blocked. You will need to contact Apple for that problem also.

There is a contact link.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat         

Apple Support using Twitter

Or fill out and submit this form.