A lot of this thread is like one person arguing that red traffic lights mean stop, others arguing that green means go. Newton, pressure, bernoulli etc all exist and all play a part. What is wrong is many of the oversimplified explanations generated by people who didn't properly understand it in the first place. People tend to seize the first one they think they understand and promote that as the right answer.
Newton: is a law of the universe. It is not optional. Lift force is generated by accelerating a mass of air downwards. There is nothing else it can come from. Whatever other explanation is used, Newton is involved.
Pressure: lift comes from a difference in pressure between the top and bottom surfaces of the wing. There is nothing else acting on the wing that can cause lift. It doesn't really matter whether the pressure below increases or the pressure above decreases, it is the difference that matters. The difference in pressure caused by the wing causes air above and below to accelerate downwards, which is required for the lift force. Likewise the acceleration produces the pressure difference. This sounds paradoxical, but the law is "every action has an equal and opposite reaction" - since they are equal and opposite, you can call either the action, and the other the reaction.
Bernoulli: The air over the top of the wing is travelling faster and has lower pressure than the air below, so this is consistent with Bernoulli. However Bernoulli is based on conservation of energy. I suspect energy is transferred from the higher pressure areas to the lower pressure areas in the act of accelerating the air, which would tend to invalidate the assumptions. Bernoulli applies as far as the bernoulli conditions are satisfied, but we don't have equal transit time, and the air doesn't always (usually doesn't?) split exactly at the leading edge. The classic explanation of the bernoulli effect is a venturi, but this is not the only situation where it applies. It's just an example that has been used and abused.
Air deflected by the lower surface: Air pressure is a result of the number and energy of molecules bouncing off the surface. A higher pressure has more molecules or more energetic molecules bouncing off the surface. So this explanation is really just a different way of saying that the bottom surface has a higher pressure than the top surface.
Some other observations:
Lift from a flat plate: Have a look at the streamlines around a flat plate producing lift. The pressure field starts to deflect the air ahead of the plate, causing the airflow above and below to be similar to a basic airfoil.
Symmetrical airfoil: similar to flat plate i.e. the airflow above and below is NOT symmetrical
Airfoil shape: The purpose is to precisely control the flow of air around the wing to reduce drag, to prevent it from detaching (stalling) over a wider range of angles of attack, and to control where along the chord the acceleration occurs, which influences the pressure distribution (centre of pressure) and how it changes at different angles of attack.
Supersonic? Way beyond my knowledge, but I think one of the keys is to shape the top surface to avoid the airflow detaching, without the influence of the changing pressure ahead of the wing modifying the airflow.
You really need to know very little of this to fly an aircraft. You need to know the effect of speed on lift and drag, why the wing stalls and what happens, the effect of surface contamination etc. Newton, Bernoulli etc are really irrelevant to the task of flying an aircraft. They are taught badly, without real understanding, and I think most pilots are confused.
* Aerodynamics is complex. I have been interested and learning about it as a hobby for 30+ years. Year 12 physics and chemistry is very helpful but the more I learn, the more I discover that I don't know. These explanations probably also have errors and inaccuracies. I have concluded I have no hope of understanding it properly, unless one day I go back to uni and study it at a tertiary level. Luckily, that level of knowledge isn't required to fly an aircraft.