Why did my software update bring update requested but refuse to update?

Lots of possible reasons -

You need to be on WiFi (or a steady 5G connection on an iPhone 12 or 13), you need 50% battery or be plugged into a power source, you need to disconnect any VPN you may have, and you must have sufficient storage space on the device to install the update. Do you see any messages on the update screen that might explain it?