Farms yield more food than forest of course as well. But what is more, the whole math of children changes between hunter gatherers and farmers. For hunter gatherers, more mouths in the tribe are a liability. Everything has now gotten harder. What few game species and edible plants in the area have not changed in number and are being demanded further.

For agriculture societies however, the planting is easy. Harvest and processing is the challenge. Tendency is to therefore overplant and struggle to harvest it all unless some crop failure or other catastrophe befalls. This keeps you in a pattern to avoid famine but also incentivizing constant population increase to handle harvest.

Now take it a step further and what might you do in times of low food output with excess males? Might be a good time for a war, spend down some of those males and maybe return some more arable land to alleviate food pressure in the remaining population. Maybe the agriculture chiefs of old didn't think in these terms so explicitly, but they are bound by these incentives and history seems to support this sort of model playing out over time.