To preface this, I already know the abridged version of what all happens in the story, and I also know what the internet thinks of Ava. So I wanted to play it for myself and see if I can find these so called unforgivable sins the character does. I'm up to Eden-9 (rescue Jakobs planet, right after Maya gets merced), and I haven't really seen anything Ava does as offensively bad yet, and I feel everyone hasn't done anything out of character.
So essentially from what I've played so far, she hasn't really done anything deserving of hate yet.
NGL I wanted to throw that kid off a fucking cliff - Maya's death is essentially the start, with Ava's insistence that she "help" directly leading to Maya having to sacrifice herself to save Ava. If that was the start of some sort of personal growth plot I wouldn't have minded, but for most (all?) of the remainder of the game, Ava is completely useless as an NPC, just being there to blame you and Lilith for Maya's death.
As a reward for sulking and blaming you, she eventually gets Siren powers, which she can instantly weild as competently as someone who's had them their whole life. As a reward for doing literally nothing else in the story, Lilith then makes her king of Sanctuary because she's a siren I guess? Any other member of the crew would have made more sense to me. Fucking Marcus has more relevent experience and motivation. She's also literally still a child and has not matured in any way since her first appearance - I assume that happens in a DLC, spin off game, or supplementary comic book, but I never saw it.
Borderlands characters aren't exactly the most deep and complex, but she gave off the most Mary Sue vibes in a series filled with Mary Sues, being a generic annoying child that's inexplicably put on a pedestal and labelled as Very Important and Powerful and Cool.
I think the other thing is that on a series with a lot of hateable characters, she's not even fun to hate. The calypso twins were annoying as shit, gloating at your cutscene induced powerlessness, but they really worked that hate and drove it home with their streamer antics. Handsome Jack has his megalomaniacal bragging that gradually turns into a meltdown, to the point that killing him ends up being as much putting him out of his misery as getting revenge. Even claptrap, who I also want to throw off a fucking cliff, finds exciting new ways to be annoying, but Ava spends so much of the story being completely inactive that it's easy to forget she exists until she turns up to receive the rewards that you did all the fighting for.