why doesn't my system preferences show a software update option in my macbook air?

Adding on to @ Encryptor5000 mentions - this link is very important for a Big Sur upgrade. Please read that page in great detail.

Should the upgrade be to something earlier ( example Catalina, Mojave etc ) this Link will lead to Older Versions. Just be sure to do All Links is Safari Only ( other will not work ).

What version of macOS is installed ? Are we confusing update which is an update within the same version of macOS and an UpGrade is moving from one version of macOS to another ( only as an example High Sierra to Mojave ??

Hi Paige N O,

The Software Update option only appears in System Preferences if you're running macOS Mojave or later. Earlier versions of macOS use the App Store to get macOS updates and upgrades.

If you're looking to upgrade to macOS Big Sur, try searching for it in the App Store. You should be able to download it from there.