my printer won't work with Big Sur.

You can try removing it and adding it back.

You can try resetting the printing system and add it back.

You can try adding it and using the AirPrint driver instead of the manufacturer's driver.

You can check with the manufacturer for new drivers.

Why it doesn't work ?

Nobody here can tell you that without more details. Printer make/model might help. Any error messages you get might help.

Please read Solve printing problems on Mac - Apple Support. It would help if you were to identify the manufacturer and model of the printer you're using.