About software update.

If you are using macOS High Sierra, you should know there are no recent updates available.

However, you may have applications that need updating, so perhaps that's the issue?

If rebooting your Mac doesn’t fix things, see if the problem still happens in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.

Please see > How to use safe mode on your Mac - Apple Support 

Safe mode disables loading third-party drivers, forces the OS to clear certain caches and logs and does other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Does the problem persist while in Safe mode?

Exit safe mode by restarting your Mac normally and re-evaluate the issue again.

If the problem is still unresolved, please return here and post a reply and we’ll see what else we can come up with for help.

Proceed with the Safe mode reboot (for Apple Silicon) that I linked above, and then see if you can update the OS while booted in that mode.

To update, please see > Update macOS on Mac - Apple Support

Please tell us which Mac model year you’re having trouble with, and what macOS version you’re running. You can find that info by clicking the  (Apple) menu at the top of your screen and then select About This Mac.

(Note- for privacy and security please don’t post your serial number.)

Regardless of the Mac model being used, the use of Safe boot, as I posted above, is a common troubleshooting step.

Can you be more specific about what software is not being updated, please?

Is this a problem with certain (or all) applications, or are you trying to update or upgrade the Mac OS?

If your MacBook Air is a 2011 model or older, then it cannot run a macOS any newer than 10.13 High Sierra.