Take a large spoon and dangle it, lightly held, between thumb and forefinger then slowly move it under a running tap...just let the water flow touch the curved surface and see what happens. You'll see a very strong demonstration of 'lift' but there is no movement of water down BOTH sides of the spoon...just the curved surface...but 'lift' is still produced.
Sails are NOT flat - they are 'cut' to have an aerofoil shape. As wind strength increases you manipulate various controls to flatten them and reduce lift to keep the boat upright - but they never end up 'flat' - even storm sails, designed for extreme wind strengths, are not flat.
Yes you can get a flat plate, give it an AoA, and get 'some lift' but efficient lift comes from accelerating air over a curved surface which produces reduced pressure - a static pressure delta - that sucks the wing up.
The spoon experiment above should prove to anyone which is the strongest force - suck or push.