... PITOT (total) pressure is dynamic pressure PLUS static. [F]or airspeed you need dynamic [] pressure [] created by the movement through the air.
Total pressure in a compressible medium is not dynamic + static pressures.
When air (M ≤ 1) is brought to rest isentropically at the head of the pitot probe, the total pressure will be given by a function such as (6) in the graphic on this Glenn Research Center page,
Isentropic Flow Equations
The subject of (6) in the above is Ps/Pt (s=static; t=total) and will always take a value equal to or less than unity. Hence, Pt ≥ Ps or Pt - Ps ≥ 0. This latter quantity, the difference between total and static pressure, is often said to be dynamic pressure. It is in fact something else called impact pressure. If you look at (5) in the above reference, which is the definition of dynamic pressure (defined in this form by Euler and not Bernoulli), you can see the difference in the behaviour of these two functions.
Airspeed indicators map impact pressure (not dynamic pressure) to calibrated airspeed. The function which provides that mapping assumes an isentropic process, meaning as given by Jetpipe that the process leading to a total pressure is an adiabatic and reversible one, i.e. heat is neither added nor removed and no dissipative effects occur. Obviously if these conditions are not satisfied the airspeed value will be erroneous. For these reasons it is quite important that both the pitot probes and static ports are designed, and located, to ensure minimum dissipation and heat addition.