Hopeless or not, we have to do it. Right now all of humanity is in a single interconnected biosphere, that is one rich crazy dickhead away from becoming uninhabitable. How many people are out there right now claiming that we can do anything we want to the Earth and humanity can never become extinct, because God? We need to get sustainable populations off of this planet and somewhere they can survive for when the inevitable happens and one of those mouth-breathing morons hits the wrong button somewhere and releases super-Ebola into the atmosphere or something.
The "we've got to get off of this rock!!!" argument is nonsensical when you consider that the Earth is currently the most habitable place within several light-years and it's been that way for at least the past 3.5 *billion* years. Just over the past 550 million years we've seen severe ice ages, runaway greenhouse warming, an asteroid impact, several massive volcanic eruptions... these events were severe enough to devastate the biosphere and wipe out most of the species on the planet, but in each case some of them survived (otherwise we wouldn't be here). It's been able to sustain complex life for at least half a billion years. Even after the Chicxulub asteroid impact, it's still got a breathable atmosphere, radiation shielding, normal gravity, liquid water, etc., none of which are the case on Mars (all you'd need to survive would be stocks of food, warm clothes, and fuel to last out the impact winter). And even before 550 million years ago, when there's too little oxygen for complex life, it's still a better option than Mars (you'd need supplemental oxygen like on Everest but otherwise it'd be habitable). You would have to do a lot to the Earth to make it less habitable than space or Mars; even with a full-out nuclear war, you've got the Strangelove option.
Looking backwards, Earth has been habitable for a very long time, it's likely to remain so for tens of millions of years more- far longer than our species can be expected to last. Looking forwards, there's no realistic scenario in which space colonies make sense:
Let's assume that we do develop the technology to live on hostile environments such as Mars, asteroids, etc. Wouldn't this exact same technology also allow us to cope with whatever hostile environmental conditions might develop on Earth?
Let's assume that we develop the ability to terraform Mars to make it habitable. Wouldn't this exact same technology allow us to terraform Earth to correct whatever hostile conditions might emerge here?
Let's assume that nuclear war or other environmental issues threaten us as a species. Wouldn't it be a lot easier and more realistic to prevent these things from happening in the first place than build some fleet of Space Arks to escape them once they've already happened?
Let's assume again we're so suicidal that we're in danger of wiping ourselves out due to nuclear war or environmental damage. Doesn't this undermine the whole All Your Eggs in One Basket argument? I mean, the idea is that some freak event might wipe out one of your baskets, but not ALL of them. But that assumes these are independent events. If people on Earth are stupid and suicidal enough to wipe themselves out, that's not a problem with the Earth, it's a problem with the *species*. EVERY human population will have those same suicidal tendencies. It's false redundancy because all your backup systems share the exact same fatal flaw.