M Ted's Orff explanation is excellent; so is his description of music teachers! I just want to add that the Orff method is full of songs- I do a modified Orff program and we sing like crazy! Also, Carl Orff never intended his method to be the only way to teach music.
Yes, Denise, the kids leave my classroom humming and singing and every few weeks we have "song request day" and there are always songs left unsung. It sounds as though your music teacher is more instrument-minded than song-minded- it happens all too often (does he/she also teach band?). Good luck this school year- it sounds as though your kids will be having a terrific singing year!