What is the reason why mathematics is taught in school?

I entirely agree with the logical thinking part, also.  For instance, you may get a job where you never have to do the quadratic formula.  But, you don't know that right now.  No one knows that while they are still in school.  But, the ability to use the quadratic formula to solve a problem, that's what's important.

Or, I describe it this way.  Why would a football player lift weights, like the bench press specifically?  If you consider it, no football player during a game is laying on their back and pushing 300+ pounds multiple times for their work.  Then, why do it?  Because it makes them stronger.  That increase in strength will make them a better football player.

So, why do math?  You are going to have problems out in the real world that you are going to have to solve, regardless of the field.  Math is the "bench press" right now.  "Get good" at solving problems now, then you will be even better at solving problems later in your own field.