well, curved swords are better for slashing attacks than straight swords, and that's the most common kind of attack to do while you're riding past somebody, so it makes sense that a horseback based culture would prefer them.
Plus stabbing a target as you're riding past it has a good chance of you losing your weapon due to being stuck in the target.
Plus stabbing a target as you're riding past it has a good chance of you losing your weapon due to being stuck in the target.