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

It is not a matter of "harder to drive" but of a "proper amplifier" to match the lower impedance.

Amplifiers have different "abilities" that need to be "matched" with any given speaker.

Amplifier match is, subjective, and, YMMV, like everything else in audio.

NO speaker has a pure 8 ohm resistance across the audio spectrum, by the way.

Speakers are also electro-mechanical .....not mechanical. 

So, when I look at a speaker with an 8 ohm rating, it is easier to drive than a speaker with a 4 ohm load. This does not make sense to me, although I know it to be true. I have yet been able to have it explained to me that makes it clear. Can someone explain this to me in a manner that does not require an EE degree?

You are in luck.  I can explain this in terms that does not require any degrees.  In fact due to the inverse law of reciprocal square roots you probably will not understand if you DO have a degree.  The first critical thing is The Gnome.  Gnomes are small and live inside your squeaker.  Gnomes all belong to the Conservative Party - they RESIST change.  If you want more resistance you must get more Gnomes.  Second critical thing is Impudence.  Impudence is the amount of resistance. However unlike resistance in a resister where there are always the same number of Gnomes, in a squeaker the amount of resistance (measured in Gnomes) varies with frequency.  A squeaker may be described as having 8 Gnomes.  In reality - and this includes my speakers - there is a variation in resistance.  So at a lower frequency the impudence dips to as little as 4 Gnomes.  The third critical component is Currant.  Your amplifier feeds your squeakers with currants.  So it goes like this:  Your amplifier feeds 8 Gnomes at most levels of frequency.  Each Gnome processes one currant at a time.  But where the impudence dips to where there are only 4 Gnomes the speaker still needs to process 8 currants.  But there are only 4 Gnomes, so what to do?  A well designed amplifier, ie one that has a lot of currants, will pass twice as many currants to each Gnome.  So the 4 Gnomes will process 2 currants per Gnome.  The amplifier therefore has to put out currants at twice the rate.    This is all known as Gnome's Lore.

Andrei_nz has said it all.  Well done!!!

+1 on that for sure :)

I thought the notion that speakers, being transducers, vary much more in sound that do amps was universally agreed upon, and should therefore be selected first. The notion that power amps vary in character as much or more than do speakers is one I disagree with.

If you have no preference for tube or solid state then this is the way to go. If you have found that you prefer one over the other then you will need to get the amp first and then find a speaker to match. That is why in most cases, you start with the amp. It is tricky- to know that amp you have to hear it in a variety of circumstances to make an informed purchase. But if you do that, you are less likely to flush more $$$$$ down the loo trying to get the system to sound the way you want it.