Hi Austin,
When a reservationist looks at availability for a flight they dont just see the codes (classes) of service that are commonly known such as:
F = first class
C = business class
Y = coach.
Within each class of service are other codes. What the reservationist sees are many codes besides these three. Various letters on the screen apply to lets say various super saver seats (in coach y cabin), such as B, Q, M, V, K, - these might all be coach seats but each one requires different rules to be met. Such as a B might be a BE7 at xxx fare with 7 days advance booking fare.
Q might be a QE14 with 14 days advance booking fare. K might be a KWE14 meaning 14 days advance weekend travel only. There are additional separate codes for people upgrading, people traveling on free upgrades, etc. (such as XF, XC), a multitude of letters for various inventory on each flight. So, maybe there are 10 "K" type fares (seats) available on a flight, maybe 50 "B" type fares (seats) available, etc.
This explains why you can call an airline and seats are available on the flight but maybe not in the "inventory" type you are holding and/or hoping to change.
Hope this wasn't too convoluted and a bit helpful.