Try opening the Terminal app and entering this command:
softwareupdate --fetch-full-installer --full-installer-version 12.1
The current Monterey installer should download
Other potential problems:
Do you have enough free disk space?
If upgrading from macOS Sierra or later, your Mac needs 26GB of available storage to upgrade. If upgrading from an earlier release, your Mac needs up to 44GB of available storage.
Also uninstall any antivirus, internet security or "cleaning" apps before trying installing again.
Are you using a VPN?
Further, you need an Apple disk installed to upgrade to Monterey since the upgrade includes an update to the Mac's firmware. That update looks for an Apple disk and write to the dick to do the firmware update. The install will terminate or freeze if no Apple disk.
Are you using File Vault to encrypt the disk? If so turn it off and then try after the de-encrypting is complete. That can take many hours.