First of all, great song. Be blessed to know you have a cool English teacher for using this song in class as poetry analysis.
The song was first performed in 1962 and the lyrics are categorized by rhetorical questions. Clearly the sentiment here is reflecting the desire for peace and general rebellion of the sixties.
The line "How many times must the cannonballs fly before they are forever banned," is probably refering to war in general. Obviously the Vietnam war didn't use cannons, so Dylan is likely referring back to either the Revolutionary War or the Civil War. In this way, he's making two statements: "When are we going to stop fighting (wars)?" But more importantly, "When are we going to stop fighting with ourselves?"