Why Do I Need An Admin Password To Delete Apps But Not One to Install? The title says it all. It's weird. You can install apps from the Mac App Store without an admin password. But you do need one to uninstall them. Why?


I know macOS is UNIX
/Applications is a system folder.
But why do we need root privileges to remove, but not to add a file to /Applications?


Example:
The App Store runs elevated privileges as do many other parts of the system. Think of a bank, typically anyone can go deposit money in an arbitrary account, but only people with permission to withdraw funds can remove them.
When any account asks to install apps, the system checks the configuration and if allowed, installs them with the permissions programmed into the package - using the App Store app”s elevated privileges, not your account privileges to do the install.
“Why did this ship as a feature?” is harder to answer since computers are designed by many people and they, over time, agree on some ways of setting things up. Your computer could be set up to not even allow non-admin to install apps, so this is more about the convention of default settings being  chosen and if you or someone else has modified those default settings. It could be changed so anyone can delete anything in the Applications folder.
Have a look at the permissions on the app or folder and that explains why some users can delete or change it and others cannot.

https://support.apple.com/guide/mac-help/change-permissions-for-files-folders-or-disks-mchlp1203/mac