I hate admitting that I'm an INFJ

Am I a jerk for being embarrassed? Am I overthinking it? I had a former coworker who proudly proclaimed "I'm an INFJ, the rarest personality type!"

I told her I was as well! Her response?

"How? We're only 1% of the population."

Nevermind. I don't want to be a special fairy unicorn. I'm an INFP now, in case anyone asks.

(I'm only slightly more judging than perceiving, anyway)

EDIT: I didn't expect so many thoughtful responses, thank you all so much!