Mirroring makes people angry

I've loved to study people since I was a kid. I took psych in highschool and went to college to major in psych but I just never finished. I've never been an evil person but one thing I enjoy is mirroring people who try to manipulate and project on to me. I do often wonder why it makes them upset? It seems like they get weak when you show them exactly who they are. They get so angry and uncomfortable. I genuinely wonder what's the cause of this. Also when you use logic against them, it's like they have no argument but to insult you and say you're manipulative. What is the cause for this???