Well, I solved the problem with their guy from customer service on the phone (Eddie, the same guy I spoke with two days before.) It turns out that the female coupling will not allow you to push in the male fitting if there is air pressure on the coupling. That is, there can be air in the tank, but the pressure to the female coupling has to be zero. It's apparently a new "safety" feature. When I turned the pressure down, everything worked exactly as it was supposed to. Since I rarely change the hose at the compressor, this additional step will not be a problem, but it would never have occurred to me that air pressure was the problem. Just pushing harder would not allow the male to be inserted. I didn't try to force and take the chance of breaking the fitting.
Other than this big waste of time and energy, this air compressor is pretty impressive and amazingly quiet. Hopefully the rest of my experience with this compressor will be a positive one. I previously asked Eddie about changing the female coupling to a normal one. He said if I did to be very careful. The manifold that it screws into is pot metal and easy to damage. My guess is that such damage would void the warranty, and I don't need that headache. I'll probably make a one foot extension hose that stays connected all the time, and I can put a regular female coupling on the extension cable. Or, I may just leave well enough alone. Maybe all female couplings work this way and it really is not a new feature. In any case, all is well. Thanks for the suggestions. I've learned more about air hoses and fittings than I ever wanted to know.