Charlie Holloway: ... Okay. Let me show you why you guys are here.
[he holds up a cube places it on the floor and opens up another hologram showing images]
Charlie Holloway: These are images of archaeological digs from all over the earth.
[pointing to the different images]
Charlie Holloway: That's Egyptian, Mayan, Sumerian, Babylonian. That's Hawaiian at the end there and Mesopotamian. Now this one here is our most recent discovery, it's a thirty five thousand year old cave painting from the Isle of Sky in Scotland. These are ancient civilizations, they were separated by centuries, they shared no contact with one another, and yet...
[he gathers the hologram images to line up and he goes through each one]
Charlie Holloway: The same pictogram, showing men worshiping giant beings pointing to the stars was discovered at every last one of them. The only galactic system that matched, was so far from earth, that there's no way that these primitive ancient civilizations could have possibly known about. But it just so happens, that system has a sun, a lot like ours. And based on our long range scans, there seemed to be a planet. Just one planet with the moon, capable of sustaining life, and we arrived there this morning.
[after Holloway has given his presentation about the pictorgrams to the crew]
Fifield: So you're saying we're here because of a map you two kids found in a cave, is that right?
Elizabeth Shaw: No.
Charlie Holloway: Yeah. Um...
Elizabeth Shaw: No. Not a map. An invitation.
Fifield: From whom?
Elizabeth Shaw: We call them Engineers.
Fifield: Engineers? Do you mind um...telling us what they engineered?
Elizabeth Shaw: They engineered us.
Millburn: Okay, so uh...do you have anything to back that up? I mean, look, if you're willing to discount three centuries of Darwinism, that's...wooh! But how do you know? Mm?
Elizabeth Shaw: I don't. But it's what I choose to believe.
Here, Elizabeth is uses the exact same answer as her father used with her. But notice the difference: Her father was referring to the existence and quality of the afterlife, something beyond our ability to observe or perform experiments upon, and saying that he chose to believe that it existed and that it was beautiful. Elizabeth is choosing to believe that the pictures in the archaeological digs were not just made by aliens - a not unreasonable hypothesis, given the evidence that Charlie has presented - but that these aliens are our "Engineers." Now if she just wanted this to be a private, personal belief, there wouldn't be a problem. But this is a belief that she wants others to believe, also. Yet she has provided no evidence or reasoning for them to accept this belief. Just her own personal decision. One wonders how Peter Weyland, the entrepreneur who has funded this whole expedition was convinced to accept her belief.
But it becomes even more puzzling when later the team that explores the planet find the fossilized remains of the aliens and conclude that Elizabeth was right. What? So they found aliens. How does this prove that the aliens were our Engineers? Later, we find out that the aliens' DNA is a perfect match to human DNA. At that point I would think this would make somebody say, "Hey, the aliens weren't our Engineers! They were our ancestors!" But no, somehow this discovery is supposed to support Elizabeth's belief. Still later, we find out that the aliens weren't very nice people, and Elizabeth undergoes a crisis of faith. Even the robot David taunts her with the observation that her God had forsaken her. Did Elizabeth think the aliens were her God? It's all a bit confusing.
At some point Elizabeth seems to realize and accept that the aliens aren't God, or not from God, or whatever. At least, there's a brief scene were she looks up and nods, as if she's somehow sorted it all out, or decided to continue to believe in God, in spite of all that's gone wrong. But we the audience are never quite sure what Elizabeth's theology had been, nor what it is supposed to be now. It might have helped if she had sat down with a good theologian and worked all this out, before making some rather hasty leaps of faith. Or at the very least she might have read what Edward Feser had to say about it.