We don't have a population problem to mean we are literally running out of space, what we do have is a FOOD problem. That problem being our current levels of food production cannot support the entire world's population on a decent diet, of course its not a problem that affects everyone for example us fat bodies here in the US. But places where the earth is naturally very unforgiving have a "population problem" in the sense that their food production and imports can't support their population, which leds to all sorts of social stagnation and backwards development. Kids for example don't go to school because they have to spend all day hunting, stealing, or managing what few food sources they have, adults don't get the education they need and don't have the time to seek "high employment" beyond finding food day by day.
So no we don't have a population problem we have a food problem, and the despite many people's claims(although I haven't heard any on this forum) that the "food production sciences" are a "mad science." I fully support the development through scientific methods including gene manipulation to make plants that grow bigger, produce more food, need less water, repeal insects, etc