Why didn't Jor-el and Lara leave Krypton with their son?

In contrast to kicker86's answer which presents many origin stories from the comics, I'd like to concentrate more on the actual movie, which for me presents its own reasons.

In the movie Jor-El explains to his son (when he meets his digitized consciousness in the old ship on earth) that Krypton and its whole society have been corrupted over time in their striving for perfection and expansion. Children were only born artificially and their destiny and place in the society was predetermined before their birth, yet Kal-El was the only naturally born child in years. This whole situation on Krypton is reflected in Jor-El's speech:

Artificial population control was established. The outposts and space exploration were abandoned. We exhausted our natural resources. As a result, our planet's core became unstable. Eventually, our military leader, General Zod, attempted a coup, but by then it was too late. Your mother and I foresaw the coming calamity and we took certain steps to ensure your survival. This is a genesis chamber. All Kryptonians were conceived in chambers such as this. Every child was designed to perform a predetermined role in our society as a worker, a warrior, a leader, and so on. Your mother and I believed Krypton lost something precious: the element of choice, of chance. What if a child dreamed of becoming something other than what society had intended? What if a child aspired to something greater? You were the embodiment of that belief, Kal. Krypton's first natural birth in centuries. That's why we risked so much to save you.

So for Jor-El Krypton and its society were doomed long before the planet actually started to destabilize. This is also the reason why he doesn't take Zod's offer to join him in rebuilding the society, since he saw Zod misguided by the same wrong ideas that led to Krypton's downfall.

And to come back to your actual question, I think this is also the reason why Jor-El didn't join Kal-El. He believed himself and Lara to also be a part and a relic of this corrupted society. And this is what he means when he says that their fate was linked to Krypton. It wasn't their whole family, but only the naturally-born Kal-El who was the chance for a new beginning. It is true that he still preserved his consciousness in order to guide his son in this task. But I think to make their actual selves disappear together with Krypton was a step and a sacrifice Jor-El and Lara had to take for a clean reset.

There have been several reasons stated in the various eras of Superman -

The classic version

However, as time ran short, Jor-El soon found that he would only have enough time to build a spacecraft to save his son Kal-El. He decided to send Kal-El to Earth, realizing he would gain superhuman powers under Earth's more intense yellow sun and lower gravity. As Krypton finally went through its final destructive stages, Jor-El and Lara placed their son in the rocket and launched him toward Earth, before they themselves were killed along with almost all the rest of the planet's population. Lara could have fit inside the rocket as well, but she chose to stay behind to increase Kal-El's chances of reaching Earth.

Byrne's Series

Jor-El genetically altering his son's fetus (gestating in a "birthing matrix") to allow him to leave Krypton (in this version of the mythos, Kryptonians were genetically "bonded" to the planet itself, not allowing them to leave) and merely attaching a warp engine to the matrix instead of constructing a ship wholesale. The result was that Kal-El was "born" when the birthing matrix opened on Earth.

Superman: Birthright

In this version, Jor-El discovers Earth moments before launching his son's spacecraft.

mid-2000's

In the mid-2000's, another new origin tale was created, basically going back to the old version with Jor-El building a rocket to send Kal-El to Earth. This time, however, Lara could have gone, too, but she chooses to remain with Jor-El on Krypton.

Superman #69 1949

Links

• Jor-El Wikipedia
• Quora
• Comicvine

This is answered in the film:

Kal-El: Why didn't you come with me?

Jor-El: We couldn't, Kal. No matter how much we wanted to. No matter how much we loved you. Your mother, Lara, and I were a product of the failures of our world as much as Zod was tied to its fate.

In other words, Lara, Jor, Zod, and the rest are all genetically programmed in the ways of Krypton. C.f., Zod's dramatic dialogue from the climax:

I exist only to protect Krypton. That is the sole purpose for which I was born. And every action I take no matter how violent or how cruel is for the greater good of my people. And now I have no people. My soul, that is what you have taken from me.

We also get a sense of what Krypton has lost in some of the banter that Faora-Ul (Zod's lady friend) throws at Kal in the middle of their battle:

Faora-Ul: You are weak son of El. Unsure of yourself. The fact that you possess a sense of morality and we do not gives us an evolutionary advantage. And if history has proven anything it is that evolution always wins.

You know that the world maker engine could be used to re-construct Krypton, right? Jor,Lara,Zod and the rest of the Kryptonians before the link (a.k.a Kal) had a natural tendency to re-create the Kryptonian way of life. Jor and Lara knew that the survival of Kryptonian way of life was ingrained into their genes. Their hope was that Kal would find an uninhabited planet which he could use to revive Krypton (I believe in this theory because he asks Kal to save earth, instead of allowing Zod to destroy it). However, regardless of their hopes, they knew that their genetic conditioning would take over. They valued life so much that they sacrificed themselves than take that slim chance. Well, that's my 2-bit.

Whatever reason you study why Jor El, Lara and the Kryptonians did not leave the Krypton is not sufficient enough. If they couldn't leave the planet, how could they send so many ships out to discover space for proper planets to continue Kryptonian race?

You might say whatever you want but this is a flaw in the script and the main reason they made all those reasons why they didn't leave the planet was that simply the movie would not be interesting enough if beside Clark as Superman there would be also many Kryptonians present. It's just much more charming that he is the only one with such powers and of course couple of his enemies with Zod as the leader!

So they made this story that they are genetically linked to Krypton, and so on so Clark would be the only one on Earth with such super powers. If many Supermans would be there along with Clark, the movie would just lose its charm, effect and strength! He had to be special, then there is all this intensity, power and drama present! Thats it.