Cannot update Mac because System Settings will not close

What "update" are you trying to install?

Is it a minor macOS update patch, or is it to upgrade to a new major version of macOS such as going from macOS 26.x to 27.x?

Is your computer experiencing any other issues and is this why you are trying to install an "update"? If so, what are those other issues as they are likely related.

Have you tried to manually close System Settings? There may be some sub-sections in System Settings where you must first click "Done" to close a subsection before the full System Settings app can be closed normally.

If System Settings cannot be closed normally (or manually), then try Force Quitting it by right-clicking or Control-clicking on the System Settings icon on the Dock, then while the pop-up window is shown hold the Option key and select "Force Quit". If you have to Force Quit System Settings, then I highly recommend you perform a normal reboot to make sure the system boots fine & you can still log into the system & everything is behaving fine before attempting another "update".

You can also press the Command + Option + ESC keys to bring up a Force Quit window where you can select the System Settings app.