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.
Honestly even if over population is a problem there are non-eugenicsy, non-coercive ways to discourage population growth. Thailand had a pretty successful campaign of encouraging family planning and contraception use that curbed their population grow.