install macOS monterey

What is the exact wording of the error messages?

Make sure that all applications on the Mac are closed (not just minimized) before clicking on Install.

What specific MacBook Air do you have?

More the existing installer, if present, which is in your Applications folder, to the trash

Try booting to Safe Mode. That boot up takes minutes and clears caches and other things that may resolve your problem.

How to use safe mode on your Mac - Apple Support

Then redownload the Monterey installer ad try installing while in Safe Mode.

If User profile true and accurate MacBook Air 13″, macOS 11.5 ?

If Yes, have seen several persons attempting to upGrade to Monterey from a Not Totally Up to Date version of previous versions of macOS.

In this case Big Sur 11.5 is out dated as the current version is Big Sur 11.6.3

Suggest updating Big Sur to latest version before attempting the upgrade to Monterey.

It tends to give better results