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Again, lack of balance and proper strategy is the issue here, the Au Ra would need far better tactics than just "Women on horseback because they'd be fast. Men on defense because they're strong" because we'd get to a "Unstoppable force vs Immovable object" situation. Now, say if we mixed Auri men into offense (Possibly by breeding horses to be bigger, considering in FFXIV the same is done with Chocobo) they might have enough strength to pierce through the defenses. And while I can't think of a reason to have the much less stronger Auri women on defense, the point is, if you're going to be fighting war, you're going to need to be the best. Best in speed, best in strength, best in defense, and best in tactics. With the physical structure of the Auri women being so weak looking currently, it doesn't add up for them to be in a society that focuses on battle
Again you keep trying to bring in genetics when you have no knowledge of history, physiology or physics A larger horse cannot have the endurance or speed of a smaller horse. That's not possible outside pure magical fiat. The sweetspot of speed and endurance is something that would be perfect for females. You can't just make an animal bigger without it having to move greater mass, and while it might be stronger it will have less endurance.
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Sedentary life =! larger more muscular bodies, otherwise the Domans wouldn't be midlanders, they'd be highlanders (Keep in mind the highlanders in Ala Mhigo probably have their body shape due to how militaristic their society is focused). Sure the more readily available food source would allow for a more healthier life, but due to the fact that Raen seem to be far more peaceful (Ie that "Embraces a life of tranquility" bit), there wouldn't be societal push to be as strong as you could, after all, who cares about being strong whenever you don't have to worry about life or death situations?
Sedentary life style DOES mean that. That's what the real world shows. Nutrition is a really big part in why people get taller and stronger. If you'd like to try and argue purely from in game stuff go right ahead but stop using genetics in the case as you're clearly ignoring most real world stuff already.