Why can't I install iOS 9.3? I saw an update for my iOS 9.2.1 device to iOS 9.3.

However, it said that the update cannot be verified, although it was downloaded.

I even deleted all data and applications from the device, but I still cannot update the device to 9.3; it just says "Your software is up to date" on iOS 9.2.1.

Can you force an update to 9.3?
Apple yanked iOS 9.3 (13E233) for almost all devices on 03/24/16 which means you can't install it. And no, you cannot force an update to iOS 9.3 since Apple is no longer signing it.

Update: iOS 9.3 (13E237) has been released on 03/28/16 for most devices, so you should be able to download the new firmware and install now. If you still can't install, you likely have one of the few devices that still don't have an updated version of iOS 9.3. You can check your device's signing status here.