Mail cannot be opened because of a problem. Check with the developer to make sure Mail works with this version of macOS. You may need to reinstall the application. Be sure to install any available updates for the application and macOS.

You need to reinstall Catalina. Installing the update would only replace Mail if there was a Mail update in the update installer.

Reinstall El Capitan or Later Without Erasing Drive

Please be sure you back up, if possible.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid button in Disk Utility's toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Install OS X and click on the Continue button.

The current Catalina installer should install 10.15.2. If it does not, then you will need to download and install the MacOS Catalina 10.15.2 Combo Update again.

If the above does not fix your problem, then you will need to do an Erase and Install.

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.