Do you all remember when Aqua met Kairi and Aqua said this line right when Kairi's grandma came:

“Kairi, about that light--”? Personally, i think that Aqua was either gonna tell kairi about the keyblade or the inheritance ceremony that just happened when kairi was being chased by Unversed. What do you all think?

tutti frutti. I would have to agree with BondlessHero on this one. In short, Kairi was in danger and Aqua, along with Mickey, jumped in to save her. In the heat of the moment, I didn't think that Aqua would have noticed that Kairi had touched her Keyblade at the time, which did unintentionally give Kairi the ability to wield the Keyblade. Even though Kairi is a wielder, without a Keyblade as of now, she could become better if she had one on top of having experience to fight.

 

Also, consider that she was about to name Sora as her successor later, so she probably didn't realize she did it already for Kairi. Just had to say that