I found an excellent (and short) oneshot about why Aerith knows how to use a staff.
Slum Flower
Sometimes, just like she knows how to nurture a plant into flowering, she knows not to go down this or that street, or to put on a hood to hide her face in shadows, or to walk stooped and giggle crazily so the roaming packs of bored young thugs and Shinra militia will look elsewhere for entertainment.
Sometimes she doesn't.
Sometimes she doesn't know that it's going to rain, and she's just as surprised as others when dirty water starts filtering through the Plate; sometimes she doesn't know what is hidden inside a seed and instead of a fruit she gets a vegetable.
She doesn't know, this one time, that she shouldn't have stepped there, it's just a normal street and a normal day and she ends up running home with her arms crossed over the torn front of her dress.
Her mother has tried very hard to shield her from any awareness of sex, but it's everywhere, in everyone, every animal, every plant. She's always been aware of the cycle, in some way - seduction, conception, birth, growth, seduction; she just grew along her understanding of it. So when she realizes that while she's still slender and cute and non-threateningly tiny, she's also developing actual cleavage - when she pushes her arms together and leans forward, at least - she also understands that often, being a woman means having men want you.
Some men are good, and some are not, and in the Slums there are many who are not - many who have been refused so much that they believe they should just take instead of ask or they'll never have anything at all, and many more who wouldn't have asked even if they'd grown elsewhere.
And her white Materia still refuses to do anything, and Shield orbs are rather expensive, even if she wanted to risk climbing up to the plate to look for a shop that carries them. And she doesn't weigh enough for her punches to do much of anything. It made the guy who tore her dress laugh.
She doesn't like the idea of cutting up people - she would want to fix them - so knives and swords are out. She can't aim worth beans, and constant refills on munitions cost too much, so guns are out too. But the road sign at the end of that metal pole she picked up off the ground did build more than enough momentum to crash quite nicely in that man's face. And she appreciates the extra reach.
So sometimes, when she's done caring for her flower patch inside the church, she finds a broken off shingle, a broom handle, and she swings it around, and she learns how to keep her balance. She's never going to be great, she thinks, but all she asks of it is the ability to keep out of arm's reach of those rare people she's unwilling to touch.