Why should antenna loading coils have a high ratio of reactance to resistance?

The ratio of a coil's reactance to its resistance is known as its Quality Factor, or Q. In antenna design, the primary purpose of a loading coil is to provide inductive reactance to cancel out the capacitive reactance of a physically short antenna, bringing it to resonance. Ideally, you want maximum inductive reactance for tuning with minimum electrical resistance. Resistance in the coil turns your valuable RF energy into waste heat (I^2R losses) instead of radiated signals. Therefore, a high ratio of reactance to resistance minimizes these losses, maximizing the overall radiation efficiency of the antenna. While it is true that high-Q antennas have narrower bandwidths, selecting "minimize the Q" is incorrect here. The question specifically asks about the coil itself, and deliberately using a lossy (high-resistance) coil to gain bandwidth is a terrible tradeoff that severely reduces your radiated power.