It is absolutely not a fact. There is nothing inherent about any human being that causes damage to the environment. It’s what human society as we organize it does, and a very small number of people do an incredibly outsized proportion of the damage. Focusing on things like birth control and overpopulation is a major part of ecofascist rhetoric. It is also very much about punishing a distant other because after all, if you really believed that all human births were inherently damaging to the environment, we wouldn’t be having this conversation as you would have already undone the damage caused by your own parents. But you haven’t, and nor should you for many good reasons! Those reasons also apply to everyone else too.