One aspect that differentiates this film from previous tellings of Superman's origin is that a great deal of time is spent on Krypton before Jor-El fires his son into space. General Zod also realizes that the planet will be destroyed and is staging a military coup that involves chasing Jor-El around on pterodactylesque things. This whole escapade adds a much needed breath of fresh air, but why is Zod after Jor-El you ask?
You see in this continuity Kryptonians have long ago taken to genetically engineering all of their offspring to fulfill specific societal roles. Zod and his friends are designed to protect Krypton at all costs, and he's of the ideological position that certain other genetic lines should be discontinued when they find a new home. Jor-El's very unhappy with all this genetic engineering stuff (and in fact his own son is secretly the first child in centuries created through some good ol' fashion Kryptonian lovin'), so he refuses to work with Zod and instead steals "The Codec," an artifact that houses all the data for future generations of Kryptonian test-tube babies, and inexplicably destroys it by encoding the information onto his sons "cells" before sending him off to Earth to start a new beginning.
Jor-El's strategy raises several questions. Seeing as it can be safely assumed that humans do not possess the means to create a new generation of Kryptonians using the Codec (assuming they would want to), it's puzzling that Jor-El seems to think that sending his son off with it will somehow lead to a new beginning for their race. But even if Superman somehow obtained the means to utilize this Codec, all that it would let him do is create a bunch of genetically designed Kryptonians that Jor-El is seemingly against to begin with. Indeed when Superman discovers a hologram of his father's consciousness on Earth, Jor-El gives no indication that he wants Superman to create more Kryptonians, and he certainly doesn't mention that "by the way, you have a bunch of data written on your cells that is the last genetic record of your people!"
Which raises the question: why did Jor-El go to all the trouble of stealing the Codex in the first place? If he merely didn't want Zod to have it (and just felt like dooming his entire race), would it not have been a lot easier to simply destroy the Codec? And if he only wanted Superman to have the Codec (for whatever inexpiable reason) presumably Kryptonian technology is advanced enough to maybe have a copy-paste feature that could avoid destroying the original (and likely his species' only chance at salvation)? It would seem that if Zod was engineered to protect Krypton at any cost, Jor-El must have been engineered to provide the villains with a MacGuffin at any cost.
But the madness certainly doesn't end there. After Zod and his pals show up on Earth, they discover that the Codec is written on Superman's cells and that they must capture him dead or alive to retrieve it, despite the fact that they make this discovery after having taken a sample of his blood! Or do you need all of his cells?! One might assume that a hidden message would want to be written in someone's DNA or something, seeing as cells have a habit of dying and replacing themselves. The only conclusion I can come to is that perhaps Kryptonian cells do not die and that Superman has retained each individual cell that the Codec was written on when he was a baby. Perhaps when he decided to (somehow) shave he was unknowingly committing genocide!
Assuming that retrieving Superman's body will be no trouble, Zod sets about terraforming Earth so it can be a new Krypton, which will have the unfortunate side effect of wiping out all human civilization. No particular reason it needs to be Earth though. You would think that perhaps he could choose an uninhabited planet to terraform (seeing as Earth would be de-inhabited anyway) and Superman might even help out by turning over the Codec (i.e. himself) in order to save not only the Earth but his own race as well! Presumably there would need to be something preventing Zod from simply choosing another planet since this would lead to a rather unexciting climax (or maybe Zod just really hates human for no reason), but this solution is never even proposed or mentioned by anyone.
Zod's right-hand woman named Zodalina (maybe) does tell Superman that morality has been "evolved out of" Kryptonians, which is a fantastically stupid statement for three reasons:
1) "Morality" is an evolved trait that allows us to live and work together in groups. Lack of morality is a trait of lower lifeforms (for example, slugs are total wankers).
2) Nobody with the goal of creating a perfect society populated by superior beings would ever intentionally engineer them with no morality. Psychopath Land is not even a place you want to visit. (Psychopath Land might be L.A.)
3) They clearly do have a morality. Their extremely central moral precept, which they will do anything to follow, is to protect/reestablish Krypton at any cost. That is their moral imperative. The only character in Man of Steel with no discernible morality is Jor-El.