I had this experience not too long ago. I asked her a question and she said "It's a big secret for me. Let goof your male pride and beg me to answer it."
I said "Excuse me?"
She said "Yeah."
I said "If it's that bad then you don't have to tell me."
She quickly tried to spin it as a joke.
I just eyeballed her, didn't say anything and left.
The next day she brought it up again asking why I couldn't take a joke.
I told her that was not a joke. I have never asked her or will ask her to beg me for an answer and her telling me to do such a thing tells me what kind of woman she is.
Here is the ironic part, she started begging and apologizing. Saying she was really sorry and she shouldn't have said that. Blah...blah....blah. She's been really well behaved since then.
The whole thing is a power grab. A frame test. A sh!t test. She wants to see how much she can get you twisted and confused.
When you experience this, you can either strike back at her with a harder hitting comeback or you just glare at her, give her no response and go about your business.