I am not able to turn off airplane mode on my Apple Watch

Your watch will only go into Airplane Mode, using your iPhone, if you enabled this in the WatchApp on your iPhone in Settings/General/Airplane Mode -> Mirror iPhone

So, in case you can't disable it on your watch, enable to the mirror iPhone for this mode in your WatchApp, after that try to disable Airplane Mode in the Control Center of your iPhone, which should then disable it on the watch.

Did you already force restart your watch and try again after that to disable Airplane mode in the control center?

Restart Apple Watch - Apple Support

Are you able to get to the Control Center, so you can tap the Airplane mode icon?

Use Control Center on Apple Watch - Apple Support

I figure, once you “Airplane Mode“ your Phone, it will automatically Airplane mode your watch. Mine does😉.