No one has actually answered this question, so i did some research and have answered it myself as follows.
The idea that for a half wave dipole there are inductive and capacitive reactances which cancel out at resonance is false.
Confusion seems to exist because a resonant half wave dipole has similarities to a series RLC circuit.
Even though a resonant half wave dipole is similar to a series RLC circuit in some respects, the frequency of resonance for a series RLC circuit is determined by the combination of the lumped constant values of inductance and capacitance which exist inside the components, whereas for a half wave dipole antenna the resonant frequency is determined by the electrical length of the antenna elements.
For a resonant half wave dipole, the electrical length of the antenna elements is exactly one quarter of the wavelength of the applied AC electric potential. This means that AC current reflected from the ends of the antenna arrives back at the feed point in phase in time with the applied wave form. Because the voltage and current at the feed point are then in phase, there is zero reactance and the impedance at the feed point is purely resistive.
In contrast, for a series RLC circuit, reactance exists inside the components regardless of the wave length of the applied AC electric potential, including at resonance, but at resonance the combined reactances of the inductor and capacitor in the RLC circuit are equal in magnitude but opposite in sign and so cancel to produce a net zero reactance.
So for a half wave dipole at resonance, there are no reactances to cancel out, and the resonance is caused by the fact that the electrical length of the antenna elements is 90 deg or one quarter the wave length of the applied AC electric potential, which in turn results in the voltage and current at the feed point being in phase, and then the feed point impedance is purely resistive.
See this question What is the impedance of an off-center fed resonant dipole? which also helps explain further.
I hope this clears up the confusion which exists for some regarding antenna resonance.