Same here but I was on the way out and she was on the way in otherwise I would have let the door go. I've always held the door open for people, not just women. I'm a white dude and she was a black woman so my thoughts were that it was more of a racist act which kinda pissed me off more. I don't know why. Also, it's not often that I see women spit. It was weird. I was confused and a little grossed out.
The last time I held open a door for a woman she spat on the ground at my feet. Literally, spat. She never made eye contact and just had a scowl on her face. I was so taken aback I didn't know what to do but laugh. I was not expecting someone to be so miserable.
Unfortunately, some of my dumbest classmates are now teachers. I always wonder how/why did they think that they should pursue a career in education but I guess if your dumb anything can be logical.