I bought this MacBook Air in 2018 and it won't update to big Sur is it not compatible?

The model year of a MacBook Air is available at Apple menu > About This Mac.

A mid 2009 MacBook Air can be upgraded to El Capitan 10.11.6 but no later version. See: https://support.apple.com/en-us/HT211683

A late 2010 through mid 2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version. See: https://support.apple.com/en-us/HT211683

A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later. See: https://support.apple.com/en-us/HT211683

A mid 2013 and early 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: https://support.apple.com/en-us/HT211683

An early 2015 or later can be upgraded to the current version of Monterey macOS 12. See: https://support.apple.com/en-us/HT212735

If you are updating from High Sierra or later, you will need 35GB of available storage remaining on your Mac before the upgrade. Presently, you cannot get Big Sur directly from the Mac App Store, so you need to get the link from How to get old versions of macOS.

Catalina, Big Sur, and Monterey all require 64-bit applications. Perform a Time Machine backup before you upgrade, and verify with your printer/scanner vendors that they have driver support for Big Sur, or that your device is supported when networked by Apple's built-in AirPrint. No vendor drivers are necessary if supported by AirPrint.