How is school arbitrary?
While the process of gathering many children (who otherwise would not be doing useful work) to learn things is not in and of itself arbitrary, the excessive divisions created in school, especially during purported fun activities, is more than enough to bring about me saying that it is arbitrary.
For example, class. While it may have been a useful proxy for intelligence ability when school was a newer concept (especially across the entire society) it is no longer as useful, simply organizing people by age and expecting them all to have the same level of intelligence. Classes have become such an ingrained concept that there is basically no way they could no longer be part of school. It's who you are in the same room with for a much larger portion of the day than everyone else, and who you are often expected to have some form of camaraderie during designated "fun" activities created by the school staff.
Another example of arbitrariness is in the grading system. How does knowing less than 60% of the material on a test or quiz (for Americans) mean that you do not know the subject? Or for that matter, how does knowing 100% of the material on a test or quiz mean you know the subject? While I would agree that getting a 100% generally indicates knowing the subject well enough, there is nothing about only scoring a 60% (unless it is a test where many options can be guessed with a 1/4, 1/5, or 1/2 chance, which many tests are) that specifically indicates that you have obtained sufficient knowledge of the subject.