Why write? Well, why go to school? Why arrange one's furniture in a meaningful way, or bestow a name to one's vehicle? Why do anything that isn't absolutely necessary for our physical survival?
Why? Because we can, and it makes life that much more worth it. These things aren't necessary for our physical survival, but I would argue they're critical to the survival of our soul. My car's name is Gasket and Seal. My furniture is arranged so I eat in one room and entertain myself in another (also so my cat doesn't crawl inside of the couch, that's always fun).
I write because it entertains me. It also helps me remember things, and it helps me become a better person. I can build on ideas I might stumble upon, and maybe with some time and effort, create something meaningful. I'm not good with keeping momentum with projects, so the most common reason is self-entertainment. I also write music, and I rarely come up with an entire song's worth of lyrics in one sitting, so jotting down notes and ideas here and there is priceless.
There are a million reasons to write, and as long as somebody has one, that's all they need. Yes.
