So far my best bets have been talking about the Demographic Transition Model - i.e, as wealth goes up, birth rates decline, so uplift the poor and we'll be fine.
I also say that we have enough resources to go around if we stop allowing 1 man to use the resources of 100.
Theres also people with mad conspiracies that the government is trying to decrease birth rates by promoting LGBT stuff. To that I've said I also say that the current system of capitalism is all about growth and making money, and more people = more money. They don't want to thin us down.
What else can I say? It seems to be a very common belief.
Overpopulation has core truths and extreme ecofascist dangers. It is all about the framing of the problem and therefore the space of solutions.
The challenge with sustainability is that it is caused by many human activities and how we organize production, many of them directly feeding into one another, mitigating or amplifying negative impacts. For example, single-use glass bottles are heavier and has a higher GHG impact from transportation and production than plastic bottles. If we had plentiful and clean energy in production and transportation, however, the equation starts to tip towards glass (and even more so if bottles are reused). Many impacts can therefore be thought of as conditional (glass worse with dirty energy, transportation, single-usr). The flip-side is that one-at-a-time changes are marginal. If your toolkit for addressing sustainability is one thing at a time and you evaluate expected impacts independently, ya fucked up your analysis because they're not independent.
Overpopulation has this exact same problem of framing. In current conditions, if the only thing you did was decrease the population and kept everything else the same, environmental destruction would decrease, probably proportionally. This is an truth, at least so far as these things can be. You will fail to convince people, possibly even yourself, if you deny it. There are large coalitions of climate scientists who agree and publish widely on it and they're not just being ecofascists, they're trying to build plausible models and this appears as a variable.
And just like with other sustainability issues, it is almost always only considered as a marginal impact. That is how it stands out: if it's the only thing you change, it seems pretty good compared to only using a certain kind of bottle or improving housing insulation. In addition, it really stands out because you can factor in population size as impacting all levels of sustainability that involve consumption. In a world of marginal solutions, it stands out.
The first threat of ecofascism is that both psychologically and absorbed propaganda, decreasing population size immediately brings up ecofascist solutions. The most obvious are genocidal monsters, but slightly more subtle discourse will lead to it. The idea that China or India or Africa have too large of populations in particular and should be blamed for these problems and "rein in" their populations. The effect is a new form of imperialist apologetics that justifies an increase in their relative mortality. Ecofascism.
The second threat is how this framing ignores the possibilities when you move outside of marginal interventions and start thinking holistically. Holistic solutions are necessary to create a sustainable world, but they're usually ignored because they aren't just one independent variable you can tweak in a model, they're thousands of interacting ones. Ecosocialists see this in the necessity of revolution: all of industry needs to be completely overhauled in the interests of the people rather than capitalistic profit-seeking that is only good at producing a fuckload of consumer goods to our general detriment. We need to be inspecting and changing every aspect of production, including materials acquisition, parts manufacturing, logistics, agriculture, waste management, and acceptable technology use for, e.g., energy production. These things are necessary and the ecofascist consideration is to their detriment because it centers a marginal "solution" that won't actually solve the problem but will create scapegoats.
The core truth is that making these necessary changes to industrialized society will allow a much larger "carrying capacity". Therefore, the ecofascist focus on overpopulation is the image of a settler champing at the bit to massacre a bunch of indigenous people so they can eat the remaining food rather than learn how to farm. We need to learn how to farm and we don't need to massacre anyone. Let's just learn to farm.