For the same reason your bank can't test how well you store your PIN and secret phrase, I imagine. It's not in the contract between you and the bank, and the general law doesn't allow for it ("I was not trying to burgle that house, Your Honour, I was testing its security" — "That's a nice joke, mister, so I won't you hold in contempt of the court. Still, guilty, five years").
> Why can't I ask an organization I trust to test the security of my bank?
For the same reason the bank can't ask an organization it trusts to test how well you store your PIN and secret phrase, I imagine: it's not in the contract.
And good luck trying to find a bank that would agree to let you inspect their security.