For updated information on this issue, see Your IT department made a change that prevents you from syncing this folder.
Original post follows:
When users try to sync a OneDrive for Business library or SharePoint Team Site library, they receive a message “We couldn’t sync this library. This library isn’t available offline”.
This happens when Offline Client Availability is set to No.
Change the Offline Availability to Yes.
To modify setting, click the gear in the top right and go to Site Settings
Under the Search section, you will click on the link that says Search and offline availability.
Change the Offline availability to Yes
NOTE: The Offline Availability may also be set to No, under the Site Settings, Site Library and Lists
Customize Documents, followed by Advanced Settings