Although it's in every review, the main hook/conceit of the film was unknown to me when I saw it, so I could think about it afresh and on its own terms. If you haven't seen the movie yet—go because it's a conversation starter and pretty interesting—there be spoilers.
The second and third act are whether a father should kill his entire family or not. That this happens to be God's chosen son for rebooting Earth and humans 2.0 is clever but feels a little sophomoric. Aronofsky on Colbert said he had been thinking of Noah since he wrote a prize winning imaginary fiction in grade school. Maybe all that's in the movie was in there. It sounds like a hip idea a teenager would come up with: "Hey, dude, instead of the boring Bible story, let's turn Noah into a murderous villain." I can see the attraction: instead of being tested by faith, Noah is tested by humanity. He goes about this new plan after he sees what he thinks is a vision from God telling him to do it. (God doesn't directly speak to him as in the Bible but sends him lush, evocative dreams.) It's entirely up to him to figure out whether humanity should be saved or shouldn't. It's not God's command anymore. In effect, Noah has become God—believing that humanity is no good for the protection of the Earth and all its creatures, so once he safely delivers all the animals, humans should go extinct.
The problem is, the movie is pretty clearly wanting to be a environmental parable. Aronofsky has repeatedly said that, including in the incisive New Yorker profile (paywalled; check the damn magazine out from the library). He wants it to be about climate change. The issue is that the second and third acts aren't about global warming and conservation of the earth, but about a man who wants to kill his children. When Noah changes his mind and there are shots of the family setting up house on a beautiful verdant hill, there's a montage of animal parents with their young. Then, you go, oh, wait, I forgot about the environment when Russell Crowe went all Stepfather for. In other words, that montage isn't earned except for the theme of parents loving their children instead of killing them. The environmental allegory hasn't been developed and brought forcibly home to the audience.
There's a larger problem: this is a religious movie and has been marketed to Christians. Now generalizations aside, if a lot of evangelical people think God wouldn't let anything happen to the Earth, and therefore there's no such thing as climate change, seeing a guy who is prepared to slaughter his family, and thus make the entire human race cease to exist—to that Christian moviegoer, Noah comes across as mad, a kook, a radical environmentalist. Especially in the end when the movie says God didn't want Noah to have done what he considered. Instead of doing a clear parable about the dangers of global warming, Aronofsky decided to be cool-clever by having a twist. It's a shame—and probably I'm exaggerating the problem—because the movie is very made well, a offbeat farrago of other genres and literary ideas, with an arthouse sensibility.