Often, presta valves stick. The symptom is that the pressure jumps to a really high number, way over 100 psi, on the first downstroke, since air isn't going into the tire. So get in the habit of "burping" the valve, unscrew it and give it a quick tap to let a tiny amount of air out. Now your pump will work correctly.

You seem to be having a different problem. Do you flip the lever to lock the pump head onto the valve stem?

Sometimes, people really jam the pump head onto the valve. You don't need to shove it down hard.