Oh, Ghostwriter, Ghostwriter, Ghostwriter...
When will u guys learn?? The #1 (or at least one of the top rules) you should know about women is that giving them ultimatum or straight-forward statements about what you will or won't accept will NOT make them learn their lesson OR do what you want them to do.
You know what you COULD have done? Instead of sounding like an insecure wimp by verbally expressing how pissed off you were, you COULD have just done the same thing to her that she was doing to you.
In other words: you COULD have just found another girl "friend" you're close with, and start hanging out with her more. Then, when your girlfriend started questioning you about all the time you were spending with this other girl, you COULD have given her the same B.S. lines she was giving you (i.e. "Oh, we're just friends, we've known each other forever, she's not into me like that," etc.)
At some point - if she really DID, in fact, like you - she would have given you the speech you gave her. At which point, you could have said: "tell you what, let's make a deal: I'll spend less time with (name of girl "friend") if you agree to do the same with (name of her guy "friend"). That way neither of us will have to question our feelings for each other."
And BOOM! You'd still have a GF that wanted to spend time with you, and you wouldn't have come across as insecure.
But now, who KNOWS what will happen? Answer: I do, and it ain't gonna be pretty!