Well, you are right. And I agree. Although in my defence, he made the initial claim without further evidence.
Anywho, the Food and Agriculture Organization (FAO), an agency operating under the UN, has done plenty of research and published papers about this.
The conundrum lies in that while we need more effective food production, we also want everything to be grown naturally (without fertilizer and/or free range livestock etc.), which is ineffective.
We need more land for crops and animals to feed more people, but we also need more space to house those same people, meanwhile we cannot continue deforestation.
On top of those, soil needs time to replenish all the nutrients. If it's not given that opportunity, it WILL become permanently unusable.
There's simply too many conflicting wants and needs that are strictly incompatible.