In the very long term, the survival of the human species depends upon developing the capability to colonize other planets. Earth is always vulnerable to major asteroid and meteor impacts, and there will come points billions of years in the future when the carbon cycle ends and when the sun becomes a red giant.
As of today, however, humanity has more pressing problems. Indeed, it is not at all clear that humanity will be able to survive the next few centuries. We continue to abuse the planet – exhausting non-renewable resources and accumulating dangerous wastes. At the same time, the world is still wired up for a Dr. Strangelove-style nuclear war, with thousands of cities incinerated with thermonuclear bombs, followed by nuclear winter.
In a way, perhaps overcoming those challenges and any others that arise in the next few centuries will be an important test for humanity. If we were to spread through the galaxy now, we would arguably be spreading as a malignancy: a species that cannot manage itself, and which brings the risk of ruin to any place it visits. If we can spend the next few centuries producing a global society that is safe and sustainable, perhaps we will have gained the maturity to carry something valuable outwards – something that better represents the potential of humanity, when compared with the messes we have produced for ourselves at this stage in history.