Au Ra physiology and other lore.

[Cilia]

Unless those girls are also the ninjas and being petite helps in stealth during assassinations. I'd have a hard time taking a male Au Ra seriously as a ninja in the same way I doubt many take male Roegadyn seriously in the same position.

What about Elezen of either sex, highlanders and Roe Females?

Well, that's... a bit contextual. As it stands, pretty much any race is going to be a better assassin in Eorzea than the Au Ra, purely because they're so few in number. Assassination requires either being able to blend in or remain undetected; the former is highly difficult for the Au Ra in present Eorzea, even in "casual" clothing. Stealth is something every ninja is trained in, but if we were to go with "realistic" stealth / assassination missions (a la my favorite stealth game ever, Deus Ex: Human Revolution), you'd need to be good at hiding. Otherwise, we've got Assassin's Creed-style assassination / stealth missions, and to do that you need to be able to blend in... which no Au Ra can presently do in Eorzea.

The present "stealth" mechanics don't... don't count. A toggle to be invisible isn't proper stealth. You only get one proper stealth mission as part of one NIN quest.

The Ninja fighting style, though, is another matter. Due to its emphasis on acrobatics and swift movements, a more trim physique is probably best for being a Ninja. Elezen would have no problem with it, since they have very lithe physiques, and despite being a bit bulkier than Midlanders Highlander Hyur shouldn't have too much trouble with it. Roegadyn of both sexes are rather stocky, and due to the extra energy required to move all that mass probably aren't well-suited to the job.

That's not to say a character can't break the mold (female Au Ra Dark Knights, Lallafell Warriors, Roegadyn White Mages, etc.) and for gameplay purposes any character can be any class, but... yeah.

If archery would be so preferred method of combat, then why aren't the boys also just as lithe and small? Warfare isn't a subject of preference really, it's what works best, there wouldn't be a case of "woman preferring archery, men just don't" it'd be "archery is more effective, you will learn archery as your main technique" applies to both boys and girls.

Well, it's a little complicated and we need more information. We don't know how long ago it was, but it's very likely that the Xaela are the Au Ra "template," so to speak, and there simply hasn't been enough genetic drift since the Raen split from them to show any major differences. Perhaps the women are all cavalry and the men make up the bulk of their infantry? /shrug