My imac won't let me eject a CD.

Try restarting and keep the mouse clicked down while it is starting back up. Hope that does the trick.

1. eject discs using the F12 or eject key on the keyboard.
2. If the disc will not eject try dragging the disc icon to the trash.
3. If the disc will still not eject, holding down the trackpad or mouse button after restarting the computer should also eject a disc. (As suggested by Ben Rigsby)
4. If the disc continues not to eject, reset the Power Manager (PMU) or System Management Controller (SMC) and try steps 1-4 again.

This is one of my favorites:

Create a burn folder or open Toast if you have it, drop some data in it and press the burn button. The disc will pop out.

remembered another one. open terminal and type drutil tray eject and press enter/return.

Those are the only 5 ways I have ever known/read to eject a stubborn cd/dvd. Sorry 😟. You only other option may be to take it to an Apple store or AASP for service/repair.

Same story for me. I put an older CD in with various data file types I meant to copy to my hard drive and it just swallowed it--Finder doesn't recognize there is a disk in the drive, none of the fixes above work...what could have happened?

Try opening Terminal and type: drutil eject

Press Return

If it still doesn't eject, then open Disk Utility. Do you have a Superdrive listed below the Mac HD? If you do, click on it and then click the eject icon at the top of the window. If you don't, did you reset the SMC? If you reset the SMC already, check to see if the Superdrive is listed in System Profiler or System Report. If it isn't, it's time for a repair. If it is, then try in a new user (I doubt it would be user specific if you can't even eject it from Startup Manager or while holding the mouse/trackpad button during startup).

Gute Nacht.