If your trying to convince a Frenchman in to something, its like you're
Why would you say so? The French education system is baded for a good part on competition and debating skills, so debating is a second nature to us.
I'm not saying Shiro is completly wrong, just that I'm more right
. The use of sword/straight sword doesn't come only (and perhaps not mainly) because it's used on horse or not.
First, there is a logical error in saying
"Mongols used curved swords, since they rode horses"
Logically it means "Horseriding --> Curved swords"
But as "Frankish knight ride horse and straight swords", it disproves the logicial link suggested by Shiro.
So we need to find the truth somewhere else.
Second point from Shiro: They use a curved sword because they will slash and not thrust, while with a straight sword you thrust and don't slash.
I suggest you read this interestin article
The straight thrusting sword can be traced back to the straight two edged sword of war of Mediaeval times. Originally a cut and thrust sword, the adoption of plate armour led to specialised thrusting forms being produced
http://swordforum.com/articles/ams/cavalrycombat.php
The straight thrusting sword also possesses a number of advantages. If faced with an armoured foe the thrust is the only sword blow likely to result in decisive wounds. The thrust is also the only blow to which the forward movement of the horse can be directly applied
Interestingly, the famous Polish winged hussar used both
The Polish hussar would use his thrusting sword if obliged to charge after his lance had been broken; if he was involved in a melee or was fighting in a less ordered formation he would rely on his sabre
So I stand by what I said earlier: the development of armor and fighting style (heavy cavalry charging vs lightly armored cavarly "harrassing") as much more importance than the simple "they are cavalry, they have curved sword" statement.