Mac OS Won't Update

Download the Security Update from here,

https://support.apple.com/kb/DL2079?viewlocale=en_US&locale=en_US

Once downloaded double-click to install.

Your 2012 MacBook Air cannot install macOS Big Sur, your mac does not meet the hardware

requirements for Big Sur.

macOS Big Sur is compatible with the following computers. 

MacBook introduced in 2015 or later

MacBook Air introduced in 2013 or later

MacBook Pro introduced in late 2013 or later

Mac mini introduced in 2014 or later

iMac introduced in 2014 or later

iMac Pro

Mac Pro introduced in 2013 or later

View the complete list of compatible computers.

Ignore what the App Store says, it is wrong and has been wrong for a long time

I have a 2010 Mac Pro and the it definitely cannot install Big Sur but the App Store

says Works on this Mac Pro.

Firstly the Apple update for Catalina Security Update 2021-004. Suggest Manually download. And Stop there. Check how much Empty Space is Available on the computer. About this Mac >> Storage tab. How much empty space ?? - post back the results.

Reason asking to do this step is because you tried to download Big Sur and that gave an Error Message. From my experience - this error message may indicate several things Including but not limited to Lack Of Empty Space.

Try deleting useless files and Emty the bin, then Backup Data Factory Reset mac

( Backup so you Don't Loose All you files And everything) Sign In And Check, If still Continues, Report To Apple Customer Care

(Because Theres No Other Way LOL)

You couldn't have been told that Big Sur was available for a Mid 2012 MBA because the max OS it can run is Catalina, 10.15.7: