The main reason for a subject change request to be denied is usually timetable-related. Timetables are constructed using "blocks" and if the subject you want to change into doesn't fit in with the rest of your subject combinations, it usually isn't possible without you shuffling around other subjects as well.
In terms of class sizes and if they come back and say that, unfortunately there isn't much you can do. If your school is a government school, the agreement actually mandates class sizes so no government school can go over a certain amount. If independent, I am sure whatever agreement they are under would contain something similar.
An option you can explore is doing the subject via VSV (dist ed). Unfortunately constructing a timetable is a really bloody hard job, trying to balance student desire vs. the smooth operation of a school (e.g. staffing, class numbers, etc). Not everyone is going to be happy.