Some cards cannot be sold. For example, if you make a bunch of treasure cards (say 50 of them), sometimes they cannot be sold. You either have to use them or sell them. If they are the type that cannot be sold, the only alternative would be to trash them.
I do wish they could be fed to pets though. Feeding a TC to a pet should give you a single point of pet training. Just like feeding some clothing articles sometimes gives you from 1 to 4 pet training points - it should be extended to treasure cards also.
Why would you even trash treasure cards when you can sell them?
Sometimes you have 999 treasure cards and 450,000 gold. When your gold is maxed, trashing treasure cards is easier than selling them. Though to be honest when you have 200 Polymorph Ninja Pig, 200 Triton, 200 Feint, 200 Tower Shield, and 200 Cleanse Charm treasure cards, walking back to the Bazaar, buying the most expensive piece of gear you can find, selling it back, and then selling the cards does take less time than trashing that many.