This is the best way to ferret out narcissists. You cut ties, but they don't necessarily hate you. They just forget you exist. At least until they need something from you again.
Unfortunately, I had plans to meet with a friend for lunch - and that friend was moving away the following afternoon. When I told my coworker that I was not going to attend the meeting during that time under any circumstances he lost his shit ...and I calmly and sternly told him he can take it up with my boss.
I walked away from that conversation thinking "well shit, it was fun while it lasted", Surprisingly my co-worker cooled down, dealt with the meeting situation, and never said a word to my boss. To boot, he _never_ lost his shit like that with me again and we've had a pretty good friendship ever since.
When I start getting a certain vibe from some people, I start countering requests with similar but slightly smaller requests. Amazing how so many people can demand another's time and resources but refuse to return anything themselves.
Often even making that straight-faced, respectful, comparable request will end a relationship. It's sad but it must be done.