IMO, the claims that population is the problem is far more dangerous. Population growth is mostly a solved problem. All population growth models have the growth being much slower over the next 50 years than it was over the past 50. Most viable models actually show the growth reversing, and some even show it peaking near current levels.

Does that mean we've fixed the problems? Far from it.

The number of people is only a really small factor in the damage that people do. One jet-setting westerner does many orders of magnitude more damage than the typical subsistence farmer; and the damage done by subsistence farmers varies quite widely. (Some are causing desertification and chopping down trees)

And of course there are some people doing more good than harm, reducing the population reduces those people too.

No matter what the population is, we have a lot of work to do. Greenhouse gases are the most visible problem; there are lots of others.