My Imac which is operating on MacOS Big Sur will not update to the newest Mojave. It just spins when checking for updates

You are confused, Mojave would be a downgrade from Big Sur. In other words Mojave is older than Big Sur.

Please tell us the model year of your iMac. If you are unsure please the  in the upper left of the display and then click About this Mac and it will tell you the model year of the computer.

If you are attempting to update to Monterey (the version of Mac OS after Big Sur) and you are not able to please follow the instruction below:

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 attempt your update and test.

I am running Catalina on a 2019 imac and since the 2-22 security update, my software update is showing notification but in my system preferences the software update just continually spins. I'm in safe boot and having the same issue. I have not installed additional software/peripherals or updated any existing since the sec. update.

jgm77,

Please either execute the steps provided or create your own thread. What you are doing which I am sure is unintentional is called threadjacking. In short you have a similar symptom to the OP however your issue may be totally different. So trying to handle both you and the OP becomes very confusing. Therefore it is wise to simply create your own thread if the problem persists.

Monterey, not Mojave, is the latest macOS version.

What iMac sub-model? These are the supported Macs for Monterey:

You must have a LATE 2015 iMac or newer to install Monterey.

As mentioned in my first post, please restart in Safe Mode and then while in Safe Mode execute the update to Monterey.