"The planet has been through a lot worse than us. Been through all kinds of things worse than us. Been through earthquakes, volcanoes, plate tectonics, continental drift, solar flares, sun spots, magnetic storms, the magnetic reversal of the poles...hundreds of thousands of years of bombardment by comets and asteroids and meteors, worlwide floods, tidal waves, worldwide fires, erosion, cosmic rays, recurring ice ages...And we think some plastic bags, and some aluminum cans are going to make a difference? The planet...the planet...the planet isn't going anywhere. WE ARE!"

- George Carlin

Should we then stop worrying about child predators, terrorism, property theft and rape because in the big picture we will all be dead soon anyway?

What a ridiculous suggestion. Of course we shouldn't, because those things affect us in the present.

The destruction of the environment affects us at the present too

We probably still have a few thousand years left. We're not going extinct tomorrow.