- Not a requirement. I'm not into forcing kids to do anything unnecessary for life.
Okay so. First of all, knowledge is power, and like Eris said, learning about other cultures and other skills, etc. Is really important. But there's also a scientific reason why.
The arts improve your cognitive function (including attention span, ability to comprehend information) and brain development. Things that kids do when they do art stuff develops fine motor skills (painting, drawing, even dancing). Creating art and dancing develops your brain better than it would without this training, by lengthening your attention span, and further improving your ability to process information. Researchers have found that people who do performing arts "differed in many white matter regions, including sensory and motor pathways, both at the primary and higher cognitive levels of processing".
Here are a few (credible) resources backing me up on this:
http://www.aasa.org/SchoolAdministratorArticle.aspx?id=7378
http://www.dana.org/Cerebrum/2009/How_Arts_Training_Improves_Attention_and_Cognition/
Performing arts also improve your public speaking skills. Performing in front of an audience at a young age gives you the confidence to effectively speak in public.
Here's the source on this:
https://www.washingtonpost.com/news/answer-sheet/wp/2013/01/22/top-10-skills-children-learn-from-the-arts/?utm_term=.2e98761824bd
The arts aren't unnecessary or not a requirement. Besides learning about new things, they also shape the way a child's brain works, and how they perform later in life.