This is a thesis in medieval history. The stirrup, invented somewhere out east, India perhaps, the steppes perhaps, came to Western Europe in the 700's. We have contemporary painting, carvings and such, some show riders without stirrups, some show riders with stirrups. Which makes us think the stirrup came into wide spread use after 700AD and before 800AD.
In case you have never ridden a horse, I can tell you that stirrups on your saddle make all the difference in the world. With stirrups your seat is firm, firm enough to rope cows and drag them to a halt, firm enough to wield a sword, and especially firm enough to couch a lance, and stay on your horse after you hit the other guy. Without stirrups you are riding bareback, and all the rider's attention is devoted to staying on the horse. Wielding edged weapons or even shooting arrows bareback is just not practical.
Which is why cavalry was a minor force, used mostly for scouting up until the time of Charlemagne. Charlemagne's cavalry were the first equipped with stirrups, and they conquered all of Western Europe. Armored cavalry dominated European warfare up until the infantry were issued muskets sometime in the 1500's. Frankish knights on the First Crusade easily swept Muslim opponents from the field. When the Franks lowered their lances and spurred their horses into a charge, look out, nothing could stop them.
Armored cavalry are far more expensive to equip than infantry. The horse is costly, so is the armor, and other gear. So expensive that the land of Western Europe was divided into fiefs, each big enough to support a cavalry man, who was planted on the land as a nobleman. Which lead to the nobility of Europe, who called the shots and ran things up until the French revolution, and in some countries far later. This was called the feudal system.
The feudal system was standard thinking among medieval historians, until the 1970's. They were teaching it to my daughter at John's Hopkins only a few years ago.
Now the bulk of medievalists no longer believe in the feudal explanation of European history. They have a new thesis, which I do not understand, but they are all very set on it.
And so, on a medieval history mailing list, we have the following topic getting discussed, "Can educators really affect willful ignorance?" The gist of this thread is plenty of students come into the class believing in feudalism as a thesis, and still believe in it at the end of the class. Teaching of the alternate thesis doesn't take. And this is just dreadful. I'd be more sympathetic if I even knew the name of the alternate thesis, even more if I had read a good explanation of it, in a hard back book. I'm a history buff, and had such a book come to my attention I would have read it.