Why On a half-wave wire the current is maximum at the center and drops to nearly zero at the ends, while voltage is maximum at the ends. Impedance is voltage divided by current, so feeding at an end where current is near zero gives a very high impedance, typically a few thousand ohms. That is why end-fed half-wave antennas need a matching device such as a 49:1 transformer or a parallel tuned circuit to work with 50 ohm coax.
Watch out Approximately 50 ohms describes the same half-wave wire fed at its center, where current is high and voltage is low; that is the classic dipole feed point, not the end.
Ends of a half wave are voltage peaks, current nulls: high V over low I equals high Z. Center feed low Z, end feed high Z.