Why can't I install an free antivirus software?

You must have administrator privileges to install software packages. See System Preferences : Users & Groups : Allow user to administer this computer.

If that is already set, then reboot your Mac in Safe boot mode by pressing and holding the shift key on restart until you see the customary progress bar. This will be a slower boot. Can you install Malwarebytes in Safe Boot mode? Reboot normally, and try to install Malwarebytes if you couldn't in Safe Boot mode.

If you deleted an important file, how would I know what you deleted, and what impact that might currently have?

As there are no viruses on the Mac, installing any anti-virus product is a step backwards in its bad interaction with the built-in security measures in macOS. Years of posts here by those that impacted the proper operation of their Macs by installing _____ anti-virus product. Just don't do it.

The biggest threat to your Mac is you. Click the wrong confusing green button on an untrusted website, or the wrong download on aggregation sites, and you may install adware/malware that can ruin your day. For that, I use — like many others here — the free Malwarebytes for Mac product — without vendor compensation for mentioning it here. It is a 14-day free trial that has realtime malware detection built-in. After the 14-day trial, the realtime features cease, but you can interactively scan for malware with the product. If you want that realtime feature back, it is an optional subscription.

Consider it a gift...

You really don't want to install antivirus software. It serves absolutely no purpose. There are no viruses in the wild that can affect macOS.

Antivirus software will cause more problems than it can solve.