Why can we kill another user's process while shutting the system down If I try to `kill` root's process or another user's process it says you can't do this. But I can do that while shutting the system down. Isn't this a security problem?

Those systems that let unprivileged users shut down the system usually only do it for users that are logged in locally, that is, users that have physical access to the machine and could for instance just as well pull the power chord or press the power button/switch.

In that case, it's better to let them shut down the system so it can be done gracefully and so that we have a record of who triggered the shut down.

Where the source of electrical power can be secured and access to the power button removed to regular users, it's generally possible to remove that possibility.