Disk Utility "Couldn't unmount disk" in Recovery Mode

You have hardware problems.

Make a "Genius" appointment at an Apple Store.

Back up all data on the internal drive(s) before you hand over your computer to anyone. If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.

Keeping your confidential data secure during hardware repair

*An SSD doesn't need to be zeroed.

As the recovery partition is in fact part a hidden partition on the hard drive you are trying to reformat, this can sometimes create the behavior you describe. While there is definitely a problem, you could be lucky and just have a case of messed up formatting.

See if you can boot from another media like an external hard drive with a system clone or a USB drive with an OS X installer on it. Then from there, run disk utility again and see if it allows you to reformat. If no external boot drives are available then you can also try Internet recovery which basically loads the recovery partition from Apple's server (slow process). To do this, boot your Mac holding down the Command and R keys simultanously. I dont know if this will default to the local recovery partition or force an internet connection, maybe Linc can clarify.

If the greyed out partition still has it's original name (like Macintosh HD) it may not be as serious, if the greyed out partition has a weird name that is not one you set then it may be more severe. Either way, as mentioned, prepare for a Genius Bar visit but try reformatting from another media first as it gives unrestricted access to the internal drive. This has a 20-30% success rate in my experience.

You may have more than one issue. I can't be more specific.

I had this same issue. All I did is restarted my computer while holding down Control+R to go into recovery mode. Opened Disk Utilities and clicked "Repair Disk Permissions". Then after that the issue got corrected.

Command-R while rebooring will take you to recovery mode.

This thread hasn't been posted in in a while, but I just wanted to add that when I erased the disk selecting the zero out option, it let me erase it. However, when I simply selected erase, I kept getting the couldn't unmount error. Really strange, but I thought I'd share in case any one else googles this problem and needs solutions! This worked for me.

Thank you for that post. I had a similar problem with a friends MBP, started from recovery to erase and reinstall, in my case just erase worked out. Interesting your case, good to know.

And when working on my own MBP in Target Mode, the solution to can't unmount was to put the disk in Spotlight of the accessing Mac into the Private Sphere of Spotlight preferences, so the background indexing did not avoid the unmount.

I ran First Aid once. It failed with the same message. Then I tried it again, and it succeeded (and unmounted at the same time). Then I was able to erase the disk. Success!