He said this process of itch is trying to constantly open my game. Could this be? What can he do to resolve this?

Although this screenshot shows that the game has been downloaded with the itch.io app, that seems to be something purely between Avast and the game's setup file.

I'd suggest contacting Avast about this: https://www.avast.com/false-positive-file-form.php - that form only allows uploads up to 50MB, so you may have to find another channel to reach them :(

I do have one actionable piece of advice: instead of distributing an InnoSetup installer, just push the game's folder using butler, as recommended in this guide:

• Distributing windows build for the itch.io app
• You can get started quickly with butler by following this guide

Best of luck solving this particular AV issue! Getting rid of the installer altogether might be enough to fix it. Installers tend to request administrator privileges for no good reason, and antivirus software tends not to like that.