It's more of a class system that Fiora goes against.
is a commoner, so she isn't tied into the noble traditions.
is a half-dragon from outside of Demacia...I keep thinking that most Demacian nobles see her as
's pet or something, which would probably piss
off.
Was forced into military service. She didn't choose her position.
I think the women of Demacian Noble families are expected to be used like bargaining pieces (which is how women have been used a lot in history sadly) and thus are meant to follow the house rules and be "a good wife/daughter". They have no choice in their lives, or rather their choice is obey or bring shame down upon your family (and shame is kryptonite to noble families).
basically said, "fuck that". She did it for selfish reasons sure (she makes a better Noxian) but she did defy the noble traditions of Demacia and has made it work. Though her short story indicates that people still don't take her seriously (and they pay dearly for it if they ever duel her), so she's constantly working to bring her house back up to glory. Fiora didn't want to ignore the traditions of her house, she wanted to actually be a part of the choices her house takes (that and she liked fencing too much to really ever give up on that) which she couldn't do as a bargaining piece.
Now directing this towards her rivalry in
, I think (And I know people hate this, but
is older than she was originally. I'm willing to say late 20's or early 30's)
see's a lot of potential in Lux and it pisses her off because Lux is all too willing to submit to the whims of those around her. Fiora probably sees Lux as wasting her gifts and probably makes it a point to verbally attack her whenever they meet for political/noble family business. Because she pities her and probably wants to her to crack (because Lux suppresses her emotions on a heavy scale, she's lying to those around her and herself. Fiora can see through it and wants to shatter it).
This is mainly my headcannon. I just keep imagining Fiora getting slapped by Lux after a large verbal beatdown, only to have Lux freeze in place with a look of terror on her face with the realization of what she has done.
And then Fiora smiles, "Finally awake, Miss Crownguard?"