You may have asked yourself this question at one time or another. It's like a child's question such as: why is the sky blue? We grow grass for one reason: we can mow it and it survives, even thrives. Any other plant, even most other grasses would die after being mowed with any regularity. There are over 10,000 species of grass, yet only about 50 of those are suitable for use in a lawn.
Why can lawn grasses be regularly mown without dying, and still maintain a healthy and attractive appearance? Unlike most plants, lawn grasses grow from the base of the plant, well below the sharpened rotating lawn mower blade. Other plants grow at the tips that don't respond well to being repeatedly cut.
The process of mowing is actually reducing the plants leaves and cutting down its ability to use photosynthesis. Photosynthesis is the process that takes carbon dioxide from the air and turns it into carbohydrates that the plant uses for food. When the plant looses some of this ability, it overcompensates by producing additional leaves. The result: an even thicker, denser lawn.
So, the answer to the question "why grow grass?" is: because it's the one plant that adapts best for the environment we've created for ourselves.