Imagine pulling a fixed walled tube though the air, the air will move through the tube at roughly the speed that the tube is pulled through the air.
Now imagine pulling a funnel that starts off large and gets smaller. The same air will now have to move faster to get through the funnel (higher pressure at the mouth of the funnel, lower at the end).
It's not a good explanation intuitively because it's not clear why that has to happen, and it's just wrong, because that doesn't happen.
On the one hand I agree that it is a stupid way to phrase it. On the other hand if the air doesn't "make it" then there is nothing where the wing just was aka a vacuum. The low pressure area that forms above the wing sucks the air along making it faster. Why doesn't all the air rush to fill the low pressure area? Well for air below the wing there is a wing in the way, air above the air flowing over the wing does rush down to fill the void providing lift, air behind the wing does as well creating some drag.
Same for angle of attack it deflects the air that would normally be above and behind the wing down (providing some lift),making a low pressure area form above the wing which the air speeds to fill.
Just a nitpick, but these forces are never pulling, only pushing. The air rushing to fill the voids is not pulling the wing, is the air below or in front if the wing that pushes (and doesn't find an equal push on the other side).
The best I could arrive at was that the forward motion of the wing causes the back side of the curved wing top simply to pull away from the air in that region, reducing the pressure there, and incidentally (because Bernoulli) that air then moves faster as a result.