To see why Bradbury gave his story this title, just look at the poem by Sara Teasdale that the house recites before the fire starts.
In this poem, Teasdale is saying that nature will not care at all if human beings cease to exist. If people vanish, the Earth and all the other creatures would continue to exist and would probably do so quite happily.
In this story, Bradbury is showing us how our technology is starting to make this a real possibility. He is saying that we are gaining the power to wipe ourselves off the face of the Earth. If we do, however, we will find (actually we won't because we won't exist) that we are not really that important -- life on Earth will continue without us if we are so stupid as to make ourselves extinct.