"Air flows faster on top" is the Bernoulli explanation. The Bernoulli principle tells us that fast air means low pressure, and low pressure sucks the plane up.
Newton explanation is the idea that the wing pushes the air down, and by reaction, pushes the plane up. Based on Newton's third law.
In reality, both are correct. The Bernoulli explanation is more specific and the Newton one is more generic. But if you want the whole picture, you need the Navier Stokes equations. Unfortunately, these are very hard to solve, so even engineers have to use simplified models.
I personally prefer the Newton explanation. It explains less, but the Bernoulli one is confusing and results in many misunderstandings. For example, that air takes the same time to follow the top side and bottom side of the wing, which is completely wrong.
The common depiction also tends to hide the fact that the trailing edge of wings is at an downwards angle, even though it is the most important part. Nice profiles make wings more efficient, but the real thing that makes planes fly is that angle, called angle of attack.
Focusing on the profile rather than on the angle of attack leads to questions like "How can planes fly upside down?" (the answer is "by pointing the nose up", and that should be obvious). If you are just trying to understand how planes fly, forget about wing profile, it is just optimization.
I want to go up. I want to use the thrust I have available to achieve that. Would not the most efficient use of the thrust available be the direct and naive approach, of pointing the engine straight up/down? Nope.
Instead, we point the engine horizontally; literally orthogonal to our desired goal. Then we use these "wing" things - they're not complicated, they're just rigid bodies with a shape, which honestly isn't even that unusual of a shape. Now we're not only able to go up (we finally achieve our goal), but we get to go fast in some horizontal direction as well.
I haven't found an explanation for this that feels satisfying to me.