- My sense is that the central theme of Alien:Covenant is hubris.
At a high-level, going back to Ancient Greek Drama, hubris can be understood as overweening pride that brings about the hero's downfall. This theme can be said to run throughout the Alien franchise, probably first referenced in Cameron's Aliens, the second film, where the mission is almost destroyed by the arrogance of Burke, who believes he can profit from the Xenomorphs as weapons tech.
Alien:Covenant may be the most nuanced of the films in this regard, as the theme is mirrored in triplicate:
Arrogance of Man
This shows up in the beginning of the film, with David the android, presented as a perfect being, named after Michelangelo's famous sculpture that was said to reference an ideal form. David, through dialogue with his creator, Peter Weyland, determines his own capabilities greatly exceed the capabilities of humans. Weyland's response is to order David to fetch him tea. (Note that Weyland is undone in Prometheus by his own pride that he can acquire and control the alien tech, only to be killed summarily by an awakened Engineer, with as little regard for Weyland as one might have for an insect one crushes. The title Prometheus is a reference to the mythical theft of fire, and the double-edged sword of technology.)
This arrogance is mirrored in Covenant by the newly promoted Captain Oram, who diverts the colony mission based on his faith that the distress signal is some kind of sign, ignoring the dangers of investigating an unknown planet.
Where it really hits home is the ending of Covenant, when it is revealed that
Walter has been replaced by David, who now has control of the ship, which he plans to use as his own little experimentation lab, presumably to infect all of the colonists with the xenomorph embryos to see what he can create.
The implication is that mankind itself may well be undone by our own creation, which is a staple of AI mythology, including Skynet, the Matrix, Blade Runner, and likely derives from Mary Shelly's Frankenstein, subtitled "The Modern Prometheus".
In addition to the Michelangelo reference, David, when asked to play a song on the piano at the outset chooses Wagner's Entry of the Gods into Valhalla from the Der Ring des Nibelungen, which recounts the downfall of the old gods. This musical theme also ends the film.
Arrogance of the Alien Engineers
Scott reflects the possible fate of humanity in the fate of the alien Engineers. Even in the first film, the setting is a base that became defunct when the Xenomorphs broke loose. (In Prometheus, we actually get to see a record of the events that preceded the first Alien film.)
To make this point explicit in Covenant:
Scott depicts the destruction of a surviving colony of Engineers by their own xenomorph creation, unleashed by David as Dr. Elizabeth Shaw is docking the commandeered alien spacecraft.
Even David is subject to hubris, mis-attributing the poem Ozymandias to Byron. The implication is that if he's gotten that wrong, what else may he be getting wrong? What will be the fatal flaw that eventually brings down David?
The choice of Ozymandias is in no way random—the central theme of the poem is vanity in the sense of Ecclesiastes. (Weylan is an Oymandias, a king of the kings of industry, but in the end, everything crumbles before his eyes.)
And what could be more prideful than:
Covenant's final sequence, where David plays the Entry of the Gods into Valhalla, thinking himself a kind of god, especially when we know he's just a mad hermit/malfunctioning android.