I have a Mac Book Pro (A1278). It will not let me download the latest version of Big Sur. Do I have to get a new computer or is there a way I can get this latest version downloaded?

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 2009 MacBook Air can be upgraded to El Capitan 10.11.6 but no later version. See: How to get old versions of macOS - Apple Support

A late 2010 through mid 2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version. See: How to get old versions of macOS - Apple Support

A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later. See: How to get old versions of macOS - Apple Support

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