Some believe we should limit growth now, thus potentially preventing the problem before it becomes, well, a problem.
Nobody is suggesting nobody has children. People will still be born, discoveries made etc.
Inequality seems to be deeply encoded in the system. Capacity, in my opinion, only makes sense if you extrapolate from an average human, but there is no such thing as an average human being. However, I don't think it is an exaggeration that our western way of life is not sustainable on a global scale. I wish the fruits of human ingenuity could be enjoyed by every single one of us, but unfortunately it seems utopian.
Even the poorest in our society have incredible access to goods.
Just to list a few:
Wikipedia
Ability to talk to relatives from across the world to little or no cost (Skype and alternatives)
Ability to send money and store wealth cheaply (low cost ETFs, bitcoin, free checking)
Social acceptance of previously marginalized lifestyles
Access to wide variety of foods and entertainment
There has never been a better time to be alive, and I expect that to continue, despite greater inequality.
What will need to change is the efficiency of how we as a species make use of the earth. We can feed many times the current world population easily. We can house many times the current world population easily. What we can't accomplish is doing those things the same way we do things now.
Advances in agriculture, energy and housing are needed. Advances which are happening as we furiously type at each other.
Either we all die horribly or we'll all be fine.
Example:
> In a 1994 study titled Food, Land, Population and the U.S. Economy, David Pimentel and Mario Giampietro estimated the maximum U.S. population for a sustainable economy at 200 million
The dangers of over-population myth assumes a naive view of a static society. For instance, we can reasonably have X land for food production, from that we can grow Y food and that can feed Z people so anything above Z would be harmful. The problem is that Y is dependent on human innovation and technology. Same can be said for most resources. We never did reach peak oil.
These predictions of inevitable decline have been wrong for a long time. I don't know why you put so much faith into the modern day equivalents.