Two Factor Authenication Troubles
Check for Two Factor Authentication and turn off:
Check if you have the Two Factor Authentication enabled on the account, if yes disable that. For some reason (which should have been fixed long ago) Mac's seem to have an issue with Two Factor Authentication.
See the tips here:
In the office 365 account.go to account help, go to view my Microsoft account, go to security info,then cancel 2 step verification. (quoted from a Microsoft answers user.)
(Instructions given to Original Poster on Answers Forum by Apple Technician, when contacted Apple.)