The premise of the whole series. Humanity has some incredibly advanced technology, including but not limited to: the means to build a 28 km long ship capable of lasting over a thousand years, incredibly advanced mechs, and planet-cracking missiles that would put the Death Star to shame. And they're still on the run, because as powerful as humanity is, the Gauna still have the upper hand.
Sidonia itself is an ongoing symbol of just how desperate humanity is. Compared to similar ships from other franchises, such as Galactica or Homeworld, it's easily the least well equipped for its mission: preserving humanity. There’s no inertial dampening, no hyperspace, its radio communication is purely conventional, and it looks like it was torn apart and rebuilt multiple times. On top of that, there are no other space stations, no civilization, of any sort they can retreat to. If their ONE ship fails or gets destroyed, that’s it. There’s simply nowhere to retreat to.
The series has probably one of the bleaker depictions of space, and worse yet: its unusually realistic. Their last contact with any other human ship was 100+ years prior to the series. The reason was due to the physical distance between the two ships being so great that their communications tech couldn’t compensate. Whether or not they’re the ‘last humans’ can’t be confirmed.
Imagine knowing someone and you both get on two different generation ships. You’re pretty much guaranteed never to see them in person again. Then the distance between the two of you become so great that communication signals are no longer reliable. Eventually, nothing. There’s no closure to this outcome. The other ship either died, or the signals stopped working. Sometime in the future, your distant descendants might meet with the descendants of the other ship. By that point though, the two cultures will probably be so different, they’ll treat each other like aliens.
"The Moment of the Bisection of Earth". Prior to the events of the series, Earth was somehow split in two perfect halves by the Gauna during their assault on the planet. It puts the odds humanity is against in perspective: what can a handful of seed ships do against a force that can accomplish that?
To prevent a Gauna from reaching Sidonia, Kobayashi is forced to order an emergency acceleration. The arificial gravity system become unable to compensate for the acceleration, causing the residential blocks to crumble and many to die falling to their deaths. The scene is all the more horrifying in the anime, where scores of people "fall" sideways, almost evaporating as their bodies slam into the sides of buildings at incredible speeds.
Kanata is driven mad because he saw his mother, and unleashes his Gravitron Radiation Emitter. The ensuing blast is shown over six pages and punches a hole on a faraway moon.
Nagate, the hero of Sidonia sees A LOT of combat once he’s recruited. Is he its trump card? Is he just that awesome? Does leadership want him dead, and the most politically viable way to do so is to make him a casualty of war? Is his squad leader sabotaging his efforts in the field to get him killed, or at least destroy his reputation; at the expense of the lives of their squad mates? If you guessed those last two items, welcome to humanity.
The Guana’s favorite pastime is trying to imitate humanity... to disastrous and disturbing effect. The whole conflict began when a Guana tried to form a humoid, the size of a city, and then dropped itself on a city. From the brief photographic visual, it looks like a giant corpse falling from the sky. The first time the series shows a real Guana encounter, it promptly eats a pilot and then begins to reform itself in the pilot’s shape, with the same corpse-like outcome. It consumes a possible love interest, and reforms her, more than once. One looks human enough to become a false hope spot. The other becomes a meat puppet Blood Knight responsible for possibly the most human casualties of any Guana in the timespan of the series.
It gets worse: Four copies of Eiko, the first pilot mentioned above, are built to replace Benisuzume 10 whole years after her assimilation. The Gauna knows to hold a grudge and may or may not hold the actual key to transcendence.
