I think it's easier to think of inverted flight as normal flight for a negative AoA. If the airfoil is symmetric -- as almost all aerobatic aircraft's are -- then it's functionally identical and inverted flight becomes a coordinate system "trick".

My favourite two "explanations" of flight are 1) dP/dt for air is greater down than up; and 2) Kelvin's circulation theorem, but alas that one is not very pub-friendly...