Below is a copy-n-paste from the earlier part of this thread where I posted screenshots and a list of what worked for me. Hopefully this will get you going in the right direction...
I was dragging the .vcf files into the "empty" column where Contacts should appear, which wasn't working.
Then I tried dragging the .vcf files into the very far left column directly onto the toggled "checkbox" labeled "Address Book." All of my .vcf files appeared and worked.
In my case, I was using Entourage and needed to move my contacts list to the new Outlook for Mac 2016. The new Outlook doesn't support importing in traditional methods. So, in summary...
• From Entourage, I clicked "Address Book" to view all of my contacts, selected all and dragged them to a folder on my desktop (this gives you a .vcf for all contacts).
• I then opened Outlook for Mac 2016 and clicked the "People" tab (which appeared in the bottom of my Outlook window).
• The column Correntin noted is at the very far left with a title of "Address Book" next to a toggled checkbox.
• From the finder I selected all of the .vcf files (that were exported from Entourage) and dragged them directly on top of the words "Address Book".
This worked and tested out for me!
Click to view screenshot here.