Why does an LHCP (or RHCP) antenna reject RHCP (or LHCP) signal?
I'll admit the Wikipedia explanation makes my head spin too. Let's keep the antennas still.
Think of a pair of crossed dipole antennas just above the earth's surface. One oriented North-South, the other East-West. Connect the same transmitter to both, but use an extra piece of transmission line so the current in the E-W dipole is 90 degrees delayed relative to the N-S dipole. Presto, you have a circularly polarized transmitting antenna. Which polarization? Looking down onto the antenna, the signal is rotating from North to East (clockwise), but looking upward in the direction of propagation, it's counterclockwise or left-hand circularly polarized.
Now think of a geostationary satellite directly overhead, with a similar pair of dipoles oriented N-S and E-W (at this instant, anyway). To get the signals from the two dipoles to add up in phase at the receiver, you'll need that same extra piece of transmission line, but now it has to delay the N-S dipole relative to the E-W dipole to cancel out the delay. Otherwise, the signals will be 180 degrees out of phase. And that's why the antenna system would 'reject' opposite-circularly polarized signals.
While this sounds like the satellite antenna has the opposite circular polarization, that's not the case, because the direction of transmission/reception is downward, not upward. In that direction, it's the same left-hand circular polarization as the ground antenna.
I think...