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 conciousness 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 conciousness 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.