In my book there was a statement about agriculture: fields being SMALLER due to HIGHER population density. Shouldn't the fields be bigger BECAUSE there's more people?

Fields should be bigger to feed more people, but they are smaller because people live on those lands.

Explanation:

A higher population density means that there are more people in an area. As there are more people, there is not enough space for all of them to live in the city, so new cities and towns emerge occupying the field's lands used for cattle raising and agriculture. There should be larger fields to feed all the population, but they become smaller because parts of them are now populated.