This is a pretty standard starting point for a lot of Science Fiction. Man has to flee the Earth as it is no longer habitable. I have seen it in books and movies. Sometimes the people are leaving for a location that is habitable. Most times, however, they are just fleeing the planet in order to life in space.
Why is this a fallacy? In the case that we have destroyed the planet completely or in a scenario where the sun is about to expand and swallow us, it isn’t. Pretty much any other situation makes leaving the Earth foolish. Let us go with a worst case scenario: Nuclear Holocaust. Radiation envelops the planet. You know another place with deadly radiation? Space. You might argue that the earth is poisoned, the air, the water, the ground itself. To that I ask, “where are you going to get these essentials to go on you space station?” If the planet gets too hot or too cold, I could tell you another place with temperature extremes. Yep, Space.
Even if the Earth was a very hostile environment for life, it would not be more hostile than space itself. Instead of building a space station and further poisoning the planet transporting everyone on earth to said space station, why wouldn’t you build a secure environment on the surface of this new hostile earth. It would make sense to do this so we could have easy access to ores, water, and oxygen. I guess you could mine asteroids for ore, but then you have to get there and find one with the ore you need. Water, good luck in space. Poison water is better than no water. Air, could be manufactured with plants, but to support even a thousand people that would be a lot of plants. I hydrogen is common enough, if you could find a way to capture it, you could then introduce it into your oxygen rich atmosphere on a rainforest ship to produce water, but all of that could easily be done on the Earth’s surface and out of the vacuum of space.
Instances where leaving are the best option: Problems with the sun, the Earth is breaking up. We are over-crowded and have to get some people off the planet. To be honest an overcrowded planet would soon be fighting for resources and would not stay overcrowded for long. Governments would likely step in and control reproductive rights long before they would come up for a plan for space colonization.
Conclusion- As long as the Earth is still here it will remain populated. It could even lose its ability to support life and it would still be a better option than living in a space station.