Why the dynamic pressure is not mentioned in the explanation of lift by Bernoulli's principle?
In short, "dynamic pressure is not pressure at all" (A Princeton paper on dynamic pressure and Bernoulli's theorem).  "Dynamic pressure" is a term that designates the decrease in pressure, as a consequence of the fluid's / medium's flow velocity.

I recommend that you also examine what NASA has to say:


  Integrating this differential equation:
  
  ps + .5 * r * u^2 = constant = pt
  
  This equation looks exactly like the incompressible form of Bernoulli's equation. Each term in this equation has the dimensions of a pressure (force/area); ps is the static pressure, the constant pt is called the total pressure, and
  
  .5 * r * u^2
  
  is called the dynamic pressure because it is a pressure term
  associated with the velocity u of the flow. Dynamic pressure is often
  assigned the letter q in aerodynamics:
  
  q = .5 * r * u^2