iMac(21.5inch. Mid2014) won't update software

Hi there!

Try to update macOS in safe mode.

How to use safe mode on your Mac - Apple Support

Safe mode can help you to determine whether an issue is caused by software that loads as your Mac starts up. Safe mode prevents your Mac from loading certain software as it starts up, including login items, system extensions not required by macOS, and fonts not installed by macOS. It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. And it deletes some system caches, including font caches and the kernel cache, which are automatically created again as needed.

Once you're in Safe mode, try to update macOS.

Update macOS on Mac - Apple Support

Jack

A Mid 2014 iMac is maxed out at macOS 11.X "Big Sur" which, it appears, you are already running.

"Update" has somewhat flexible meanings. Are you trying to go higher than that, or trying to apply availble Big Sur incremental updates?