There are a host of reasons why we do what we do, but we'll try to keep this (relatively) short.
Band is typically the largest or one of the largest student organizations at any school. Music is an intrinsic component of human culture; every society on this planet has their own music that they have developed or adopted from another culture. Music is therefore one of the most effective bridges between societal and cultural boundaries. The U.S. Government has long used music in such endeavors through programs like the Department of State's American Music Abroad initiative and the numerous military bands and performing ensembles in the Army, Navy, Air Force, Marines, and Coast Guard. The universal appreciation of music manifests itself as a diversity of student involvement not normally seen in other activities. Students in programs like ours represent every corner of student body's demographics. We think this makes our experience a deeper, more meaningful one that stretches each student towards growth and a deeper understanding of themselves and others.
One of the coolest (and most important) aspects of what we do is the learning process. Study after scientific study repeatedly demonstrates that studying music, particularly through learning an instrument, is one of the most cognitively beneficial endeavors anyone can pursue. We strive to support this research by making music the center of everything we do; our students deserve to reap the unique and invaluable benefits of this activity. Through our curriculum, we work hard to develop musical literacy, fundamental skills on each student's respective instrument, and the ability to interpret, perform, and enjoy music of various kinds. You can read about the National Association for Music Education's national standards for school music here.
Music for All, Inc., a national music education non-profit that hosts events like the Bands of America Marching Band Championships and the Music for All National and Regional Concert Festivals, has an even more thorough overview of these benefits and goals in the modern school band program, which you are invited to read here.
Beyond the music, our other primary goal is to use the band experience to shape young people into strong, confident, and compassionate young adults. Band is different. We have the vast majority of our students for all four years of their high school career. We see them over half of the days of four of their most formative years of life. We travel with them, we share meals with them, and we see them at their best and worst. That's why we do what we do. We don't think there's anything quite like high school band, and we cherish the opportunity, privilege, and responsibility to come alongside these kids as they become who they are.