Frustrated
If you play guitar then there probably aren't any other band classes for you to join IE Marching band, orchestra ect. Jazz band is the only school band I can think of that would have need for a guitar player. Wish I had some advice for you...
Can't you just tell them to suck it?
blaugh I play guitar and am/was in Jazz Band, Stage Band, Concert Band, and Klezmer Band.
Tell them they need a guitarist. That you are better than anyone else (hope you are) and you would be a valuable asset to JB for these reasons...
If your teacher is like mine, they will take your well thought through argument as a good sign and keep you in.
Maybe pick up an extra instrument so you can secure a spot in one of the other bands? I never had guitar lessons at school, and it was not till a few years in that the band leaders knew I played guitar as well as clarinet, and put me in the guitar spot.
Also, suggest a guitar ensemble? They can be super cool if you get the right pieces. If you are good enough, you can lead it yourself!