The next time I need to answer a secret question that might be used over the phone I'm going to write the answer in as: "No thanks, that information is private

The next time I need to answer a secret question that might be used over the phone I'm going to write the answer in as: "No thanks, that information is private and I'd rather not share it over the phone. I know, you're probably going to say that you can't help me without this information and you're doing this to help prevent identity theft but I stand by my choice to not partake in answering your question. Can I speak with a manager?" That should make for a fun conversation.