I have seen more than enough people that claim to have no children for the sake of the Environment, only to go and buy pets and treat those like children; retarded children that will never learn to speak, walk in 2 feet, or become productive members of society, demanding constant attention for their natural lifespan, and which will age rapidly and die in their teens, - and have valuable medical resources expended in heroic efforts to futily prolongue their agony for weeks/months. You could claim that the pet dies early and does not produce offspring, but then the pet owner will likely mourn for a few weeks and then go to the pet store and start all over again.
Third world countries have the 'capacity' to almost double world population (in case of medium growth scenario, hopefully population size will plateau at around 13 billion, I do not think that optimistic rapid decline is possible without rational action of global intervention to reduce population growth [0]), which IMHO sounds catastrophic. Because for next 50-100 years global population will be increasing rapidly and hopefully will stabilise after that, without any prospects of reduction for probably double of that time frame. Even if the population will start to decrease I think it may take at least few ages to reduce population size to what is today.
[0] https://en.wikipedia.org/wiki/File:World-Population-1800-210... , https://en.wikipedia.org/wiki/World_population_estimates
About 12 years ago I proposed during class in school, that to save the planet we must reduce number of people living on Earth significantly and relatively quickly. Well the teacher thought that I was new Hitler (at least at first).
Just like you said, the point is that either people shouldn't have kids at all or have no more than 1. If whole Earth's population would do this, in 30years we will see a sharp fall in the population count. And in 60years it should be reduced by 30% at least [1].
If we will not do this now - our children, or grand children will not thank us.
[0] this is probably against HN ethos, though I couldn't resist
[1] It's completely out of my head, though if the perfect scenario would work - I guess it's a reasonable number.