Q: Why doesn't my bank finance co-ops?
A: Some banks shy away from lending for cooperative apartments. There are likely several reasons for this, but perhaps most important is that these aren't mortgages made against real estate (which is considered "real" property) but rather loans made to buy shares of stock in a corporation (which is what a co-op purchase is considered).
The risks of these loans are different that those found on traditional mortgages, since any foreclosure process would leave a lender not with real property to dispose of, but rather shares of stock -- literally, pieces of paper. Co-op loans require (very) different kinds of contracts, there are risks with regard to financial health of the corporation that owns the building (plus the condition and maintenance of the building itself), and plenty of other legal aspects that make offering and funding these loans different from traditional mortgage lending.
Unlike regular mortgages, most lenders don't make enough of these to be able to profitably sell them to other investors or in the secondary markets, so they often end up in a bank's portfolio. Most banks don't prefer to hold fixed-rate mortgages in portfolio, so you may find that in cases where a lender does make co-op loans they may only offer ARMs, not fixed rates. With all these additional concerns and low origination volumes, some lenders just can't be bothered to make them at all, concentrating instead on bigger portions of the residential market.