From FWBs to "Just Friends"...I don't want to be just her friend so I severed all ties. Am I being childish?

I was FWBs with a girl for about 5 months. She ended the "benefits package" about 2 weeks ago (since I kept pushing for a relationship). I told her that I wasn't interested in 'just being friends' (shot to the ego to be demoted like that) since it would be harder to get over her but I would gladly take the FWB option if it was on the table. I'm not rude to her at work, I smile and say hello but I never start a conversation. Am I being childish or, an AFC, by completely cutting her out or am I justified. Any feedback would be appreciated.