Why exactly does Fiora have an attackspeed slow?

to tilt me whenever i play jax

to tilt me whenever i play taric

I guess to push her duelist identity?

 Exhaust was an incredibly overloaded ability that had power trimmed down to balance it, in the form of armor and magic resist reductions and an attack speed slow. Lee Sin is a bursty, mobile jungler that is already a strong duelist early game due to his kit. Fiora is not a jungler, meaning the attack speed slow doesn't help her clear healthier. She also is not nearly as mobile as Lee Sin is. Additionally, her only form of hard crowd control is a single target skill shot stun with a relatively short range that requires her to have absorbed an enemy hard crown control with her W. 

 Her entire thematic and function is to duel people, so if you are hit by her attack speed slow, which, by the way, you can dodge, unlike exhaust, and has a travel time, unlike Lee Sin's nearly instant E, you deserve it. It also requires her to stand still to perform it, which exhaust and Lee Sin's second E cast do not. I would argue that, like Malzahar's Q for silences, Fiora's W is the fairest attack speed slow in the game.

Because she's a duelist? And she can't duel attack speed carries otherwise?

Exhaust was broken and overloaded.

Because if it didn't she'd get shit on by Tryndamere even harder than she already does 1v1 I guess.