Pretty sure op is aware of the fact that the cat is actually trying to train her to hunt, but for the sake of fml's people tend to word it in a witty way. Yes the cat is trying to teach her to hunt, but from a humans perspective it looks like the cat purposely brought the mouse in (after all her cleaning) just to have it run around and bug op and isn't trying to help catch it, all just to be a dick.

Thanks, #28 - I was about to comment to explain the phenomenon myself. The behaviour OP describes is linked to your cat's belief that, as she's never seen you catch anything, you don't know how. Therefore, by bringing you something she's hunted down still alive, you can practice your hunting skills & become a proficient hunter. This behaviour is also displayed when mother cats are teaching their kittens to hunt, so it's affectionate, but she's also critiquing your apparent lack of hunting skills. Best to prove you're a capable mouser quickly this time, while she's still waiting patiently & watching, or she'll have to try teaching you again another time.