After I login to the Facebook account and redirect to the login window in ArcGIS Pro, the window closed and ArcGIS Pro application just quit immediately.
I asked my colleague to login with the same PC with his ArcGIS Online account. ArcGIS Pro then launched successfully. I checked the license is valid, so I believe there is something wrong in the authentication step of Facebook account.
I have urgent tasks to do so any reply will be really appreciated!
I haven't tested it though.
Could you add arcgis.com and facebook.com as the trusted sites in the web browsers? Then clear browser cache and cookies, and try logging in again.
The problem was solved.
I finally created another arcgis online account(not connected to any social accounts).
Since my esri and arcgis online can still login with the facebook connected account and my organization allows me to have another member inside, I authorized my new account to be an organization member and switched the user type( NEW account as GIS professional Advanced while OLD account as Creator).
Maybe you can try this method and I hope it works well in your case!
I am a tech support at ESRI and today I have assisted a user who is having the same issue. Initially, it is a BUG and it is fixed now. The resolution is to install the patch, ArcGIS Pro 2.8 Patch 2 (2.8.2). I hope this helps and works for you as well.