@AC "Authentication works two ways."
I've been bashing my head against that brick wall for years so I'm glad it's not just me. When a Bank or some such calls me they always want to verify my identity even though they've called me. I understand you need to make sure you're speaking to the right person but I need some way to check you are who you say you are before we get on to who I am.
I've had some more pragmatic responses when I've pointed out I have no means to verify their identity and usually get a name/reference so I can call back on the main number to make sure the call was genuine but I've also had plenty that think I've started speaking in Swahili when I point out I'm not giving personal information to an unverified caller who just calls up and asks for it.