To understand why philosophy isn't taught in schools, one must start with understanding what the goals of modern day education are. I believe that these goals, rather than to create informed and thinking citizens which can meaningfully take part in political and social life, are to create a competent and obedient workforce.
Look at the way class-rooms are structured. Rather than having a dialogue where the teacher convinces the student of things, facts are merely presented, memorized, and regurgitated. Even more often students are given lists of instructions to carry out, without any discernible learning outcome in mind. This is not often the case in Math, or Science based courses, but very often in geography, social studies, and most often english. (I'm making these claims based on my memory of public highschool, less than a decade ago)
Why the exception for math and science? Most likely because one must have some rudimentary grasp of these concepts to complete ordinary tasks.
“The whole educational and professional training system is a very elaborate filter, which just weeds out people who are too independent, and who think for themselves, and who don't know how to be submissive, and so on -- because they're dysfunctional to the institutions.” ― Noam Chomsky
“In our dream we have limitless resources, and the people yield themselves with perfect docility to our molding hand. The present educational conventions fade from our minds; and, unhampered by tradition, we work our own good will upon a grateful and responsive rural folk. We shall not try to make these people or any of their children into philosophers or men of learning or of science. We are not to raise up among them authors, orators, poets, or men of letters. We shall not search for embryo great artists, painters, musicians. Nor will we cherish even the humbler ambition to raise up from among them lawyers, doctors, preachers, statesmen, of whom we now have ample supply."
- Rev. Frederick T. Gates, Business Advisor to John D. Rockefeller Sr., 191