Survival. We will go extinct at some point if we stay on Earth. The more spread out we are, the less likely any single catastrophe is to wipe out the entire race.
In the more near term... Do we really need more motivation than "because it's there"?
A nuclear holocaust would not kill all the humans. A major asteroid strike would not kill all the humans. A super-flu pandemic would not kill all the humans. A single short circuit, puncture, or virus could kill all the humans on Mars.
The Earth is the perfect place for humans to live, out of the entire universe. If we can't figure out how to survive long-term on this planet, that's why we'll go extinct.
"Because it's there" is a great reason for an explorer to want to go somewhere. But that doesn't automatically have value for the future of humanity.
Terraforming Mars would prevent a 'puncture' or 'short circuit' from wiping out its population. The goal isn't to only spread human life but all of life.
Progress is progress. Choosing to make progress accelerates the process, especially when the progress we're talking about would be the first humans on another planet (and the first known life on Mars).
Motivation and inspiration.
Since you seem big on humans being good at art and culture, consider it the most impressive and daring pieces of performance art ever attempted.
> Men wanted for hazardous journey. Low wages, bitter cold, long hours of complete darkness. Safe return doubtful. Honour and recognition in event of success.
Dead is dead, whether it is by the hands of a vacuum or starvation in the bitter cold.
Indeed. Think of it as a really good remote backup plan. Colonizing another solar system would be an even better one.
The arguments I hear on this subject really sound more like a guy talking himself into buying that Porsche (or Tesla!) than anything else.
Keep sending the robots!
acomar was discussing extinction events and you seem relate that to billions of years in the future. I find that rather incredibly odd. Is it optimism?