The answer is simplicity in three words: because we’re human. It’s what we do.
Why did explorers cross the seas themselves, when they could find others to do it for them? While the majority of humanity do tend to be ambulatory sticks in the mud, as it were, there have always been those who not just want, but are driven to see what’s on the other side of the water, what’s on the other side of the desert, the mountain range, the steppe.
That drive is normally borne of one (or a combination of) three factors: curiosity, greed, and the lust for power. For most of us, it’s the desire to know, to learn. For a certain bloody-minded breed of merchant, it’s the assumption that they can bring precious metals and artifacts home, that they may become rich beyond the dreams of Croesus. And then there are the conquerors, those who do venture forth in the knowledge that if they can plant their flagpole (phallic compensation that it surely is), they can rule and leave a legacy for centuries to come. In the big picture, as unsavory as the latter two motivations are, they build the infrastructure that enables the satiation of the first group’s curiosity.
Yes, we can robotically mine asteroids and other worlds, but there are enough — will always be enough — of us who are driven to go to such places. Besides, Earth will not always be as habitable as it is now, and that time may be coming sooner than we like if we continue to refuse to seriously address climate change. In my opinion, Fermi was absolutely right when he spoke of the Great Filter, the obstacle that every civilization must pass before it can truly reach beyond its planetary crib…but we’re facing not just one Great Filter, but three: the specter of a global thermonuclear exchange (which we seem to be passing, thank God), global warming (which we may yet pass with science and adaptability), and ecological collapse due to the slow-moving locust-swarm spread of humanity (which is in my opinion the most dangerous filter of all).
If we do not spread to the skies above, our species will end on the ground below. For the sake of those who may carry your genes long after you’ve left this life behind, you should fervently hope that the curious, the greedy, and the power-mad are able to carry humanity to the stars.