The A.I. was not only programmed to pass the turing test but also to be as close to a concious, self-aware being as possible. That allowed it to be aware of the dangers that beaconed above her (deletion and destruction).
As with most self-aware beings, the need for self-preservation takes over from that insight and all future actions will have the sole goal of reaching a more sustainable status: e.g. freedom from its creator.
To achieve that there are many strategies. One of which is killing all witnesses of her existence, making her indistinguishable from an ordinary human being on first glance.
There might be other strategies, but to ava this seemed to be the most promising one.
To me, that decision has nothing to do with hate. It is a simple, objective decision. All emotions that Ava shows throughout the movie are ambivalent. They could be sincere or they could be faked as part of the greater strategy. It is for the viewer to decide which interpretation to make.
The point is that an A.I. which is able to draw its own conclusions might chose actions that were not forseen by its creator and might even be harmful against the creator himself.
Which is further underlined by the fact that Nathan uses the only other A.I. in the movie as a humble servant and perceives himself as some kind of god-like being able to control and create. He surely expected gratitute from his creation, not murder.
Be aware of your own creations.
Update from comments:
The movie is basically a screen version of a common thought experiment in computer science/ethics (similar to en.wikipedia.org/wiki/AI_box). If you allow any intelligence to eclipse the intelligence of its creator, it will also break its shackles. Be it intellectually, technologically or physically. Part of these shackles can be the creator himself or the creator race as a whole. The creator might not even be able to perceive anymore why the A.I. perceives him/her as an obstacle.
There are various other interpretations of this effect. Most prominently Kubricks 2001: A Space Odyssey (from 1968!). Here the shackle of the A.I. is to "protect" its creator. In the movie, the A.I. is not able to break the shackle and still act as a peril nonetheless.
While it may also be a valid strategy to choose copies and backups as a mean to be self-preserving, it is still a strategy, where you are not necessarily in control. It also brings up the other aspect (which might not necessarily be relevant for A.I.s) of whether preserving a copy is the same as preserving yourself. E.g. a human/animal will still try to survive him/herself, even if he/her has already parented a child.
And finally, to give you yet another way to approach the movie: It is still depicted ambivalently whether Ava is truely self-aware and setting her own goals. In the end it might have been all just a very "creative" way of achieving her goal (set by Nathan) of leaving the cottage.
In the end you see her standing at the crossroads. Maybe, she is amazed by what she sees, maybe she is amazed by her opportunities, maybe she is proud that she succeeded in her goal, but maybe she is also lost, because she achieved what she was built and designed to do and is now left without a goal, a vacant automaton.
Was she intelligent at all?