If Montessori schools are so great, why do a majority of them stop at age 12?

Actually the majority of Montessori schools end at age 4 or 5 since the majority of Montessori schools are pre-schools. But most of the others stop at either 9 or 12.

Why?

Montessori philosophy states that as children mature so does their brain. As their brain matures, it acquires and processes information differently. Our classrooms are set up to reflect these different methods of acquiring and processing knowledge.

       Pre-school classrooms (3 - 6 year olds) - are set up so that children can
       "organize their environment'" (I call this the "what?'" stage, "What is this?"
      "What is that?" )

       Lower Elementary classrooms (6 - 9 year olds) - are set up for children
       who are organizing their mind. (The "why" stage- "Why is the grass green?"
       "Why is that a dog and that a cat; they both have four legs, hair and a
       tail?", ...)

       Upper Elementary classrooms (9 - 12 year olds) - are set up for children
       who are still looking for the answers to "why", but are becoming
       increasingly aware of their peers and the world around them.

       Junior/Senior High classrooms- are set up for students organizing their
       place in the world.  (The "How" stage. "How is this going to help me in life?")
       No longer satisfied with "knowledge for knowledge's sake", they want to know
       how this knowledge fit into their future life? In a "traditional" Montessori
       environment this is the time that the children enter an Erd- kinder
       (land-farm school). In this environment the children run a farm or a factory,
       learning to apply all the knowledge that they have acquired over their years in
       Montessori to learning first hand what other knowledge they are going to
       need to be fully functioning adults.

When deciding just how far a Montessori program will go, most schools will end at the end of a developmental stage.

Why end at all?  Why not go all the way through to the end of high school?

The problem is that in this day of college prep courses, SAT's and so on, this environment scares parents. They worry about their children's chances of getting into a good college. Enrollments in Erd Kinder's are often sadly low (there are exceptions though- Houston Texas has a very strong one), and so many schools don't even attempt them. In other places people are trying to come up with a compromise where students combine work-study programs with inquiry and research based classes, college level classes, test prep classes, and so on.