Fact: Uniforms cannot deter the larger issue of violence and drug abuse in schools.
One doesn't need to look any further than Bill Clinton's address itself to understand the hypocritical nature of this argument. To quote a few excerpts from his speech,

"Today I'm visiting Long Beach, California, a community that has helped to restore order to its schools by requiring elementary and middle school students to wear uniforms... We've all seen the tragic headlines screaming of the death of a teenager who was killed for a pair of sneakers or jewelry or a designer jacket. In Detroit, a 15-year-old boy was shot for his $86 basketball shoes. In Fort Lauderdale, a 15-year-old student was robbed of his jewelry. Just this past December in Oxon Hill, Maryland, a 17-year-old honor student was killed at a bus stop, caught in the crossfire during the robbery of another student's designer jacket." (The American Presidency Project, The President's Radio Address)

In this address, the President appreciates the efforts of the Long Beach (Unified School District) in mandating elementary and middle school students to wear uniforms. However, the examples of violent behavior that he cites are all related to students in the age-group 15-17.

Across US, elementary and middle school students are being required to comply with the rules of school uniforms, while at the same time, juveniles - who, as statistics show, are involved in most illegal activities - are being excluded. There is a consensus on the fact that bringing in a regulation that mandates uniformity across schools will do little to address the larger issues of drug abuse, gang-wars, robbing, etc. By using school uniforms as a panacea, its proponents are overlooking the root cause of the problems.
Fact: Imposing uniforms on children infringes on their constitutional rights.
The First Amendment to the United States Constitution gives every individual the right to express himself freely. By imposing uniforms on children, schools take away this right from them. Numerous lawsuits have been filed by the parents of children, on the grounds that the school uniforms as an infringement on the rights of their children. The judgment in these cases has been given after taking into account the respective scenarios, and there isn't still a universal rule on this issue.

In the landmark decision of Tinker v. Des Moines Independent Community School District, the Supreme Court ruled in the favor of the students who were suspended after they refused to remove black armbands, which they had put on in opposition to the war in Vietnam. The court ruled out that the rights that every American is guaranteed by the First Amendment to Constitution, applies to every student and that schoolchildren, "do not shed their constitutional rights at the schoolhouse gate." People who support uniforms argue that an absence of uniformity can lead to a disruption in the school. However, it has to be noted that assumption plays a larger role than prudence in this claim. A teenager who is fully clad in a school uniform can still disrupt the proceedings if he hurls obscenities at his colleagues and teachers. By denying students the right to express their personalities, uniforms not only infringe on their constitutional rights, but also inhibit the development of virtues such as diversity and tolerance in the school.
Fact: Uniforms do not take care of the entire clothing needs of children.
Uniforms may be cheaper than branded or designer clothing, but they are no way cheaper than street clothing. Thus, if you are not fussy about a particular brand, you can save a lot of money if the school does not insist on uniforms. Uniforms alone do not