The Pilgrim fathers commenced the colonisation of North America in a big way, but by no means did any sizeable porportion of the population of Europe leave. They mostly went on living their regular lives. Only a few brave or crazy sould crossed the pond. The population of Europe did not reduce because of migration, it continued to grow.

Culturally, the situation with space is likely to be similar, especially given the energy cost of putting ONE person into space.

The amount of fuel that must be burned to get one person into space is about the same as that person would use in a whole lifetime on Earth.

Now, if you want to get BILLIONS of people into space (and the infrastructyure that they need to survive), and you want to do it fast enough to beat population growth on Earth, then you've got to burn chemical energy tens or huindreds of times faster than the whole world is doing at the moment.

A few tens or hundreds of space launches every year may be insignificant in their effects on the upper atmosphere, but tens to hundreds of MILLIONS of launches?

the only way to get population under control on Earth is to balance the number of births and the number of deaths.

There are only two ways to do thius:- have fewer babies (The modern Chinese solution), or let/cause more people to die - the historical solution.

This problem is essentially solved in the first world through education of women, high quality of life, and contraception. In the third world, we face a problem that will dominate the future of the whole globe.