I like to build side projects. They let you explore and experiment with ideas and tools that you may not get to spend time on at school/work. I first learned how to program because I wanted to build a social network recreation of Urban Dictionary as a side project (It turned out as bad as you might guess). I also enjoy building side projects with the goal of making them into a company. While there is nothing wrong with working on something on the side that generates income, the problem comes when you restrict yourself from building a side project just because it may not make you money.
Working on a business as a side project, is just that, work. You have to worry about taxes, refunds, and all of the overhead of running a business. While working on something without the goal of it becoming a business can take up a lot of time, you get to spend more of your time creating something, rather than dealing with business logistics. Most side projects don’t turn into successful businesses. Most of the time it's better to start a project with the goal of creating, experimenting, and learning instead of making money. Many ideas, when first proposed, sounded like terrible business ideas (Google, Facebook), but turned out to be great, but only because the creation happened before worrying about monetization. There are also projects that would make terrible businesses (comic-sans-everything, canada-eh) but are great experiments that teach you a lot, and are fun to create. Some ideas won't ever make money, but if you limit your creation to only ideas that make money, you limit the things you experiment with and explore. The more you can experiment, the better you will become at creating things and coming up with new ideas.
Next time you think of an idea that doesn’t seem like it could become a business, build it. Experiment with your ideas without worrying about monetizing them. You will be surprised how much you learn from it.