Your fallacy is the same as claiming that we should care more about car accidents than about terrorism, because car accidents kill more people, instead of realizing that the number of dead simply isn't the only thing people care about when considering threats of this kind.
It's also unclear to me why you choose to single out space colonization when the vast majority of what most people do on Earth has nothing to do with solving the problems you mention. If anything, working on enabling space colonization is far more beneficial to life on this planet than almost every other subject on HN.
Nuclear stockpiles serve as a deterrent to aggression; the fact that the US and Soviet Union did not have a conventional WWIII between 1945 and 1990 is because both sides (and England and France) had nuclear weapons that made conventional invasions untenable.
Getting rid of "nuclear stockpiles" is a terrible idea.
Unless you're a Dr. Strangelove hoping to eventually end up in the bunker with a lot of pre-selected women (or simply falsly believing that the accidents are totally impossible) I don't understand why you'd be against the reduction.
Given the real probabilities that something can go wrong, if we don't do something to prevent it, something will seriously do go wrong, relatively soon, it's a question of time, and there's not too much of it. Only with the intentionally limited amount of the nuclear weapons the humanity can survive such an event.
Thinking of weapons of mass destruction, that HAVE been used in the past, as some forms of keepers of the peace just doesn't sit right with me.
While there is an inherent danger in having weapons capable of leaving the Earth largely uninhabitable for humans there's also a very real danger that without them the last 70 years of unprecedented levels of peace ends.
I will defer to The West Wing to explain: https://www.youtube.com/watch?v=9yUHnERJ0zs
EDIT: this one has a bit more context: https://www.youtube.com/watch?v=R2HzHSeV9v8
Yeah, yeah, but your scientists were so preoccupied with whether or not they could that they didn't stop to think if they should. - Dr. Ian Malcolm.
Our focus should not be on whether we can do something. We should carefully consider why we are doing something and ensure we aren't acting in a self-destructive way.
Even if we were to pursue a massive space race, it'd only consume a relatively small fraction of humanity's industrial capability and resources as they exist today. In the context of a long-term terraforming effort, after a significant space-borne industry has been created, these sorts of binary comparisons become all the more laughable.
Lot of people assume magical science fairies will solve this via "terraforming" or some other science fiction only idea, but more likely space exploration will remain unmanned probes if just because we aren't going to send a generation of explorers to their deaths or eventual madness.
Do social and economic factors magically not apply to people who colonize the solar system? Seems to me you now have 2 problems.
Scale is the critical thing here - even small social change at scale is hard - examples are aplenty.