I can't help but wonder how much of the gender equality in Eorzea can be explained away by the fact that races like Roegadyn and Lalafell exist. With such massive racial extremes, delegating tasks by physical aptitude makes a lot more sense than doing so through gender divides, particularly since the difference between a Lalafell and a Roegadyn is much, much larger than that of a Hyur male and a Hyur female.
However, there's also the fact that Lalafell warriors are equally as effective in the role as any of the larger races. This is, of course, a concession to game mechanics, but it can also be explained away by one's ability being determined by a confluence of aether and their ability to manipulate it. Hence, physical strength is basically completely irrelevant relative to aether malleability.
Those of you who've done the Amal'jaa beastman quests may have noted that, with the merchant goods recovery quest, he questions how you managed to carry multiple large crates of goods all that way. The answer is obvious: you're superhuman thanks to your insane talent with all things aether (which also explains why you can train any class and any job with equal effectiveness), which may or may not be related to the blessing of Hydaelyn et al. Kind of a Mary Sue/Chosen One style of explanation, but that's how the PC works in this universe, and it's probably the reason why gender equality is actually a thing here (I mean, besides just being a nice thing to have IRL).
So, in summary: the answer is aether.
However, there's also the fact that Lalafell warriors are equally as effective in the role as any of the larger races. This is, of course, a concession to game mechanics, but it can also be explained away by one's ability being determined by a confluence of aether and their ability to manipulate it. Hence, physical strength is basically completely irrelevant relative to aether malleability.
Those of you who've done the Amal'jaa beastman quests may have noted that, with the merchant goods recovery quest, he questions how you managed to carry multiple large crates of goods all that way. The answer is obvious: you're superhuman thanks to your insane talent with all things aether (which also explains why you can train any class and any job with equal effectiveness), which may or may not be related to the blessing of Hydaelyn et al. Kind of a Mary Sue/Chosen One style of explanation, but that's how the PC works in this universe, and it's probably the reason why gender equality is actually a thing here (I mean, besides just being a nice thing to have IRL).
So, in summary: the answer is aether.