Unable to repartition my data disk
To enable FileVault on a non-system disk you need an EFI partition, an HFS+ volume and a Boot OS X partition. The last one will be built while enabling FileVault.

Your disk contains none of them.

Open Disk Utility (in /Applications/Utilities), choose the appropriate disk (not any inferior volume!) and hit erase in the toolbar.

Choose a name, "OS X Extended (Journaled)" as format and "GUID Partition Map" as scheme. Then hit the erase button.

If the partitioning fails, close Disk Utility and open Terminal.app. Enter diskutil list. Then enter sudo gpt -r show diskX with diskX: the disk identifier of the stubborn disk. Below I assume the identifier is disk1.

If you are sure that you have chosen the stubborn disk (I.e. the one with the 2048  1953519616      1  GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7 partition) enter:

diskutil umountDisk disk1
sudo gpt destroy disk1


Enter exit to terminate the Terminal session and quit Terminal. Open Disk Utility again and repeat the steps to partition the disk mentioned earlier.