[simonjoe]

Well, if you're willing to accept that a wing–as described–produces lift in it's 'natural' upward direction (see other replies for some links as this step is a bit complicated), then there's only one way a plane can fly upside down. That reason is that it can also create lift opposite that direction.

Wings are not static. Wings either use flaps or some mechanism that causes them to bend that alters how much lift they produce at a given speed, angle of attack, etc.. The thing is that the reference frame you choose is important.

If you have 0 lift, you're in free fall…a phenomenon that a lot of planes can do. If you can push whatever that distortion in wing shape (flaps or bending) a bit farther, then you can dive faster than freefall, that is producing lift in the downward direction.

Now, just turn the plane upside down and do the same thing.

The freakier thing is that helicopters can theoretically fly upside-down. Same thing: if they can drop faster than free fall, they can fly upside down. The catch is that it's a VERY unstable equilibrium that is a huge stress on basically all of the parts of the motor, steering mechanism, structure, etc..

Or, it's because your parents' are Santa Claus. That's really equivalent.