In reality this is just a fantasy. It is not possible for a healthy human to really care about survival of human race in case of something catastrophic happening and wiping out humanity.
Survival of human race is very different then caring about descendants. Yet as you are live witnessing right now some people barely care about that and most people do not even think about it.
If earth to be wiped out by a meteor and there was a ship with limited space to colonize another planet people would fight for that space even if it would mean decreasing success chance of mission.
People have other reasons of going. You don't colonize during the asteroid event, you colonize long before. You won't have people fighting to go to save themselves, you'll have them wanting to go for various reasons, legacy, reputation, isolation, etc.
That being said, I don't agree with your premise that you can't be a healthy person and care about the human race. You haven't added enough to support that claim.
It was an example to point out that people may behave vicious to increase survival chance of their children or themself even if conflicts with survival chance of human race in total.
