Hi folks,
Just to throw a bit more in about a symmetrical wing producing no lift at zero AoA.
I do glider aerobatics, and have flown many times in an aircraft called the Fox. It is a highly aerobatic glider, with a symmetrical wing section (similar performance both erect and inverted).
I know that this glider is very easily stalled in a nose-up and nose-down attitude. It is a weird feeling when you drop the nose sharply, and then kick in a bit of rudder.......you flip straight into an inverted spin!
Barney