If Cafeenman wants to get
that "technical", then he is also incorrect.
If the "pitch" of the airplane is downward then more thrust makes the plane go down, not up.
So if you are trying to make this into a "Profesional"

explanation, The elevator along with thrust controls the climb of an airplane.
I guess if you want to really get technical the roll, yaw, and pitch plus thrust determines if the plane is climbing.
If the plane is on its side (Knife Edge Position) thrust plus rudder makes the plane climb.
Personally I like the original explanation as it is much easier for the beginner to understand that elevator makes the plane go up and down. If the plane is flying at a reasonable constant speed and upgright, this is completely true. The beginner doesn't need to know nuclear fision to grasp this concept.
Wings