Every time I try to upgrade to OS Monterey, I get a message that my software is up to date with Big Sur

What is the model year of your MacBook Air?

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

A mid 2013 and early 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to get old versions of macOS - Apple Support

An early 2015 or later can be upgraded to the current version of Monterey macOS 12. See: How to upgrade to macOS Monterey - Apple Support

Followup - is the user profile MacBook Air 13″, macOS 11.6 accurate ?

There are several additional updates to Bug Sur as in 11.6.6 is the current version as of May 16, 2022

What is the output of this Terminal command ?

softwareupdate -l

Does the >>  Computer Qualify for the Monterey upgrade  and if it is Not specifically listed as Qualifying - this computer can not run Monterey