I have a Late 2015 27inch retina iMac and I can't update to OS Monterey. It's on the list of compatible machines. Any ideas?

Please restart the computer in Safe Mode per the directions in the  How to use safe mode on your Mac - Apple Support link. 

Note: If you are using a wireless keyboard please either plug it in using the supplied Lightning cable that shipped with it. If you are using a legacy keyboard or a third-party keyboard that does not have re-charging abilities, please use any USB keyboard. Also note that a Safe Mode restart may require you to hold down the shift key for up to 5 minutes before the computer starts in Safe Mode. You will know it is in Safe Mode when you see “Safe Mode” in the upper right of the display.

After restarting in Safe Mode, then download and install Monterey and then restart normally and test.

What have you already tried, and what happened when you tried it?

Any error messages or diagnostics shown?

If you have any add-on anti-malware apps, add-on VPN client apps, add-on cleaner apps, or such, remove those per the vendors’ instructions, restart, and try again.