Yep, agreed. She sees him as a kid.
I'm his age, my boyfriend and I also dislike talking on the phone, yet when we've had long-distance arguments (not that we've had many, but a few at the beginning), we would call each other straight away. Arguing via text is only going to make things worse, even for phone-phobic persons like many of our generation.
OP, I can't believe you really don't see your mistake. You told her you were very upset and angry, and you refused to even tell her the damn reason. You just frustrated the hell out of her and didn't even bother to give her an explanation... basically you acted like an immature teenager who throws a tantrum and then shuts himself in his room. You need to grow up a bit. Lean how to communicate effectively.
If she doesn't want to see you, it probably means she doesn't want to deal with your drama - because she probably doesn't take you seriously. I think you should really be the bigger person here and call her, tell her you need to talk to her in person, meet up with her and tell her EVERYTHING you've told us here. Remember to not be passive-aggressive.