she didn't have any compelling reason to be doing the things she did - she was just a jerk.
Likewise, the entire have/have-not dynamic didn't work because there was no plausible reason shown for it. Based on what we were shown, the citizens of Elysium were just being dicks to the rest of humanity for no particular reason.
Here's a good article that explains why the economics of the movie don't make sense: ‘Elysium’ Wants To Be A Lacerating Movie About Health Care, But It Has No Idea Why Inequality Exists
Elysium is just as well-made as District 9 - more so, even - and although both are about one group oppressing another until the oppressed fight back, District 9 was much clearer thematically. In D9, humans oppress aliens because the aliens are downright disgusting and mostly inexplicable, and the humans are simply stuck with them with no good idea what do about it. The humans were clearly the "bad guys", but even so you understood why both sides did what they did.
But in Elysium the "bad guys" have magic machines that instantly cure all illness. Everyone has one and they've got hundreds more in reserve. There's no scarcity, or visible downside or cost or side effect to using the magic machines... and yet for (reasons?) the sky people won't let the dirt people have a single one.
There are so many compelling things they could have done with that premise, though. What if Elysium can't shoot down boarders because they don't have weapons, because they're all peaceful and loving Utopian types who don't know how awful life is elsewhere. But Jodie Foster's character has been charged with protecting this Utopia... and she resorts to whatever means she has to, a la Nicholson in A Few Good Men. They need her on that wall, they just don't want to know what she does to protect them. Maybe she doesn't like doing what she does, either.
Or, show us a good reason why Earth can't have magic medi-machines, and have the characters actually have to figure out how to fix that situation. Or ultimately realize that it can't be fixed, because resources are finite and everybody can't have everything because there isn't enough of it.
These are all issues we deal with today - we like it when terrorist attacks are prevented, but we don't like drone strikes and NSA wiretaps... or at least we'd rather not know about them. We think it's really sad when there's a famine or a genocide in Africa, but most of us don't rush over there to help or sell our cars to feed African orphans either.
So the movie could have dealt with the whole issue of scarcity and poverty in a smart, relatable way, but instead it just resorted to having the sky people be doodyheads who need to be slapped around and blown up until they share their surplus toys.
And even so... it IS one of the best sci-fi movies of the summer, right up there with so-close-to-awesome Oblivion.