Crazyprof,
You are simulating a slot half wave dipole, which is the complementary to a half wave dipole. You should expect to see, in the radiation pattern, everything but what is seen in a half wave dipole. When you add the two radiation patterns you should get very close to a full sphere. What you have works perfectly for a half wave SLOT antenna, not a half wave dipole. You can look at this link for a very brief description.
Basic Slot Antenna and Its Complementary Dipole. I also attached your simulations with an added dipole simulation.
Cesar