[1] https://ourworldindata.org/grapher/food-supply-by-region-in-...
The rate of baby production in most developed countries is near or below the replacement rate. The growth rate of these countries is almost entirely from migration. It seems to be the case that when you educate people (in particular, women), give them access to birth control, and opportunities to live interesting and fulfilling lives, enough people will choose to forgo children to make up for all the people who want children.
So population isn't the problem: equitable distribution of the resources we have is.
To put it most succinctly, if only we could just get out of our scarcity mindset and achieve a reasonably fair distribution of our resources -- then those resources are more than enough to sustain everyone, and population growth isn't an issue.
Food supplies have grown tremendously post-WWII, thanks to Green Revolution agriculture. Earth's population has doubled in the past 50 years, but food is actually cheaper than it was 50 years ago.
It's a sad state of affairs when the onus of proof is placed on disproving a myth instead of proving it.
> I'm unfamiliar with the views on this, but considering the amount of starvation in the world, this seems suspect, especially considering an increasing population.
IIRC, all recent (i.e., in the last century) starvation cases were caused by disruptive events that caused systemic failures in the food supply. For example, all recent famines in Africa are triggered by civil wars.