Why do you need to study a subject at a university level to teach it at a high school? If you want to teach mathematics at a high school for example, then why do you need to study it at a university? You will learn new stuff, but you won't teach anything of that at a high school.
On one hand, when I myself was in high school I was wondering about the same thing - especially that I learnt the whole high school material (in maths and physics, I mean) in the first year, so felt that I could have taught as well as a teacher. But indeed, as pointed out by Xander Henderson and Massimo Ortolano, only at the university (in fact, only during my PhD studies; well, in fact only as a post doc; well, in fact... hm, you get the idea) I learnt the bigger picture.

So, studies are so that if a student asks "what will I need the quadratic equation for?" you could give a better answer than "because it will be on the test".



What is a better answer in this case is a whole different issue. I have lots of friends who indeed, once they finished high school, never solved a quadratic equation again. But on the other hand, they also didn't need the knowledge about Hamlet, genetics, WW II history, etc., in everyday life. That doesn't mean that they, we, you shouldn't learn about those things. I have lots of knowledge that I don't need in my life - but I enjoy obtaining it, possessing and connecting it with other areas.