Argument with girl. Did I play it right? How should have I acted? Did I deer or Dare

Got into an argument with a coworker bitch today, heres the situation. She was cleaning the office and pulled the chairs out to the main area. I sat on the big one and she after a few minutes she rudely came up to me asked me to get up and give her the chair. I said no - and her hamster started spinning. I said ill give it to you later im using it. She kept pressuring me to give her the chair and I said no Im not giving it to you im using it right now. She tried to guilt trip me and say that im doing it on purpose to which i defended myself and caught myself in the middle of it and went back to saying i want the chair ill give it to you later. She also said" I cleaned the office and worked hard and this is your thank you?" So i said "what do I have to thank you for, i didnt ask you to do it" She didnt let go so i said fuck it and stood up and walked off. Soon as i did that she started bad mouthing me and calling me trash, little boy, not a man to which i said" yeah im a woman dont you know" and she agreed and kept saying bullshit towards me. I told her she is the one in the wrong for how rude she was when she asked for the chair and if she asked nicely id give it to her no problems but she was being a bitch and after that i said im not arguing anymore and exited the conversation. After that she started crying tears in the other room and I didnt talk to her the rest of the day.

Did i play it right?

Keep in mind all of the interaction I remained calm and had strong eye contact and I didnt raise my voice.

I feel like I could have handled it better so I need some tips and some overall tips on how to deflect properly when anyone pressures me like that.