I'm more thinking from the kid's point of view. These are the formative years when a human being develops one's own identity and sense of self-worth. Mandatory school uniforms encourage, well, uniformity instead of diversity (on a psychological level), and I doubt that's healthy for a developing mind.

In particular, justifying school uniforms because "you can't tell the rich kids from the poor kids" deprives both poor kids from learning how to positively interact with rich kids and rich kids from learning how to positively interact with poor kids. Being able to interact with people of wide socioeconomic diversity is a valuable skill.

I've also heard a lot of anecdotal evidence about school uniforms being problematic in inner cities because they'll inadvertently align with gang colors, meaning that students walking to/from school would have to either bring a change of clothes (and change at school twice a day) or risk being targeted for gang violence.