There’s a common misconception of Bernoulli’s principle that’s often used to explain how an airfoil creates lift (which I assume is the “usual theory” to which you refer), and while there are many correct (or, perhaps, more correct) ways of explaining lift on an airfoil, I think the only opinions involved are as to which explanation is best. After all, opinions don’t keep a plane in the air, physics does!
I tackled the air-travels-farther-over-the-top misconception and presented one of my preferred ways of looking at the situation in a previous post; in short, the airfoil’s shape causes a downward deflection of the flow, which, by Newton’s 3rd law, indicates that the air has exerted an upward force on the airfoil. There’s a similar useful video from Cambridge on the topic here.
Another explanation I have heard used concerns circulation and its ability to produce lift (see the Kutta-Joukowski theorem for the math). In this case, it’s almost easier to think about lift on a cylinder instead of lift on a more complicated shape like an airfoil. If you spin a cylinder, you’ll find that the circulation around that object results in a force perpendicular to the flow direction. This is called the Magnus effect and, in addition to explaining why soccer balls sometimes curve strangely when kicked, has been used to steer rotor ships. One of my undergrad aero professors used to do a demonstration where he’d wrap a string around a long cardboard cylinder and demonstrate how, by pulling the string, the cylinder’s spinning produced lift, making the cylinder fly up off the lectern and attack the unsuspecting students.
An airfoil doesn’t spin, but its shape produces the same type of circulation in the flow field. Without delving into the mathematics, it’s actually possible through conformal mapping and the Joukowski transform to show that the potential flow field around a spinning cylinder is identical to that around a simple airfoil shape! Although that mathematical technique is not all that useful in a world where we can calculate the inviscid flow around complicated airfoils exactly, it’s still pretty stunning that we can analytically solve potential flow around (and thus estimate lift for) a host of airfoil shapes on the back of an envelope.
In short, your aerodynamics professor is right in saying that there are many things going on during the flow around an airfoil. If you get a roomful of aerodynamicists together and ask them to explain how airfoils generate lift, you would be faced with a lively discussion with about as many competing explanations as there are participants. As you learn more in your classes, you’ll gain a better intuitive feel for how it works and you’ll learn more of the nuances, which will help you understand why there is no one simple-to-understand explanation that we use!**
** Lest I confuse someone into thinking that aerodynamicists don’t know how airfoils produce lift, let me add that the argument here is over how best to explain the production of lift, not over how the lift is produced. We have the equations to describe the flow and we can solve them. We know that lift is there and why. We simply like to argue over how to explain it to people without all the math.