If she doesn't do online dating, I'm assuming that means she has not personally encountered: **** pics, requests for nude pics, being called a ***** because you start shutting down a conversation, being called picky / snobby / a prude because you don't desire sexual relationships with every other guy who visits your profile, etc. I don't do online dating either, and I do have a friend who met her husband via online dating and they are happily married with children, but these are things I've gathered from my female friends who have done this. I know it can lead to good things, but it's often problematic and certainly has its own challenges, especially for women.

Honestly my first thought is that she has a brother, son, or husband who had something happen to them that upset her, and she chose to take it out on you. Regardless of the reason though, there is a lot wrong with her response to you, starting with the fact that you're the paying client and you couldn't get a word in edgewise! Your therapy session is not her soapbox.