I see two reasons for choosing different spacings between plants.
First, you can't really place plants closer than what they need to grow. You can visualize a 4ftx4ft square planted with 16 large-head-type cabbages. If the heads get 10 or 12" across, and you plant them 6" apart, by the time they're partly grown, they will be too close together and shading each other out, limiting how much sunlight they get. If one is stronger than the ones next to it, it may grow large because it gets the most sunlight for the most chlorophyll production, but it will be shading the others out and they will be smaller.
The second reason is the nutrient level of the soil. If a plant is going to grow to it's maximum size, it needs a certain amount of nutrients. If the soil is excellent, with all the nutrients, and those nutrients are available in the form the plant can use, the root system doesn't need to go too far to get what the plant needs, and you can plant them relatively close together, as long as you allow
enough room for the plant to absorb enough sunshine for it to grow well.
But if the soil is poor and the nutrients are spread thinly through the soil, the roots of each plant will have to spread out further to find enough nutrition to grow. If you planted them close together, they will be competing with each other and none of them will get enough nutrition to grow well.
It all depends on your soil and the available light.
The more you garden, the more you will learn.
Sue