What model and year Mac? What is present macOS version
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 and "cleaning" apps before trying installing again.
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.
Do you have Fusion drive? Some uses have problems upgrading Macs with Fusion drives.
If not then boot to Recovery and repair/First Aid the startup disk. You can't repair/First Aid the disk you booted from.
About macOS Recovery on Intel-based Mac computers - Apple Support
If disk OK then delete the existing Monterey installer and boot to Safe Mode, which takes minutes and redownload the installer and try again.
How to use safe mode on your Mac - Apple Support
Some users have problem with skipping upgrade versions and even not updating to the latest version of Big Sur.