Why are low impedance speakers harder to drive than high impedance speakers

For the same reason you lose water pressure in the shower when the toilet is flushed. More water is drawn, lowering the pressure in the tank. When the speaker has a high impedance, it’s like a faucet that is slightly open. The pressure (voltage) in the tank (amplifier) is maintained as there is little flow (amperage) through the piping (speaker cables). When the impedance drops, the faucet opens which draws more water (amps) causing the pressure (voltage) to drop. If the amplifier does not have enough ’pressure’ it cannot supply the current for the speaker driver to move.

That is why amplifiers that maintain voltage throughout the impedance swings of speakers are heavy and expensive. They have to act as a voltage source regardless of the current demands of the speaker. This requires a bigger transformer, bigger power supply capacitors and high current output devices to put it all togther.

gs5556,
That is a very good analogy!
I’ve often wondered why given the reality of Ohm’s Law, why do many speaker designers revert to 4 ohms rather than 8 ohms (or higher) speaker impedance. As Al noted in his reply, Ralph (Atmasphere) has pointed out that the higher the impedance load ,the lower the amplifier  distortion produced (which is a desirable result you'd think).

It would seem that a concerted effort to design easier to drive high impedance speakers would yield obvious benefits. The most logical explanation for the plethora of lower impedance speakers is that the higher impedance speaker is probably more difficult to implement to get things right and presents more design challenges.
Charles

In a related matter, Roger Modjeski of Music Reference recommends hooking up your speakers to a tube amp on the lowest impedance tap that provides the power you need. So if an amp puts out 45 watts at 8 ohms and 30 at 4, and 30 watts is enough for your needs (with the combination of speaker sensitivity, room size, listening level, etc.) with an 8 ohm speaker, use the 4 ohm tap for lowest power amp distortion and best sound. 

Charles1dad, sometimes a speaker designer will add components to a cross-over to lower the impedance  in order to make the impedance flatter/smoother. Sometimes lowering the impedance allows for more current delivery in order to facilitate stronger bass response.