Some of the reasoning behind this is historical. Modern schools in the west are actually outgrowths of cathedral and monastic schools, in which the students were mainly studying for holy orders. In such an environment, simple uniforms are a way of moving beyond materialism and ego and keeping students' focus on intellectual and spiritual matters.
In the early modern period, even though schools became independent of monasteries, many maintained a religious affiliation. In such schools, uniforms were not only part of the school tradition, but also encouraged students to focus on their studies rather than their outward appearance.
With the advent of public schools, a major concern was avoiding economic discrimination and segregation. In other words, if students all wear the same uniform, you can't tell just by looking at them, which students come from rich and which students come from poor families. This reduces the chances that students from more privileged backgrounds will be mean or snobbish to those students who can't afford expensive clothing.
Finally, the idea that you should be focused on your studies rather than your clothing still applies. If you wear a school uniform, you don't need to waste time deciding what to wear; you just wear your uniform. Ideally, you also react to your fellow students based on whether they are kind, or smart, or interesting company rather than just on whether they are wearing this week's trend.
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