I disappear when my partner sees a cute guy.

A guy recently asked my girlfriend for her number. She gave it to him. She told me right away but also said she would go for coffee if she thought it was as friends. But in their initial discussions (we currently live on other sides of the country, and she comes into contact with lots of men in her program), she didn't mention I exist. Then, the next day, two days before her plane leaves to visit me in New York, he texts her, asking her to an art show. Her reply is: "I can't because I'm going to New York and have a lot to prepare" He says lets meet up next week. She says "Yeah, that sounds nice...". No mention of my existence. Or that she has a partner. Isn't this common parlance? I feel like I mention her to everyone I meet within minutes, because she is always on the tip of my tongue because she is so important to me. This is the fourth time I have felt disappeared in this three year relationship. When we first met and were dating early on, we were at a function, and both of us were at a food table chatting, and this guy I didn't know walks up and starts talking to her. She immediately brightened up, and without introducing me, she and him walked together to another food table, as if I had totally disappeared or never existed, laughing and giggling together! Then, one day we were in a rental car parking lot, and having rented here before, I knew where to park the car. She asked, looking confused, and I pointed and said, it's right over there. Just then, this young, good looking blond guy walks by, and she GETS OUT of the car, as if I hadn't said anything at all, and asks him if he knows where we are supposed to park! When I became upset she then turned it all on me as if I had no right to have a feeling about this. Then another situation where we spent this romantic day driving up the coast, when a program member guy texted her to go out for dinner with some friends, and she says she just went up the coast and wouldn't make it back in time to go, but didn't mention that I was with her, and that that was the real reason we didn't go! And now this guy. She says, "I couldn't think of how to put our relationship into a text to him" and I just put it off to buy time and if he asks again I guess I'll have to find a way to say no" and "I don't know how to deal with this awkward situation". She denies having feelings for him but says she has a "mental attraction as a friend".... and calls this a "situation"...??? Yet when I try to say something she says she doesn't have feelings for him, but since I pressed the issue, she is now considering not coming to New York to see me, because she is angry by the fact that I am hurt. She says she doesn't know what to do. Am I really daft or does she totally have feelings for this guy? Or does she just generally not think that highly of me? Does this kind of thing happen in all relationships? I feel like this never happens in the reverse. I feel I always introduce her to new people, and mention her right away, but she seems to think that merely mentioning that I exist in passing to send a message that she is not available is this huge puzzle she can't figure out. Please help.