I would have been upset as well.
Because you said something to the new person first.
NOT EVERYONE see's it this way.
But it sounds like your gf does-and I understand, because I do as well.
If one of my guys says "I met this lady, we had a great conversation and I'm interested in pursuing her as a possible potential" all lights green.
THEN they can tell said person they are interested in dating.
When I met someone I was interested in last October; I told both of the guys before I ever made plans. We met at a convention and exchanged numbers for business purposes. I didn't even follow through with the business stuff before talking to the guys. (I quite literally talked to both of them THAT day)
After several dates, it became obvious that we weren't couple material. So-I never actually told HER that I was interested in pursuing a potential relationship. But I had ALREADY told both guys.
I think your gf may be wanting something more along those lines. (guessing obviously based upon your post)
"Love As Thou Wilt"