I think whilst you're defending yourself to the girls on here who are saying you're out of line you're missing the point slightly. These girls are interpreting your comments how your girlfriend interpreted them. whether or not that's what you meant, is almost irrelevant. Your girlfriend took them badly and the situation has to be resolved. Does it matter whose 'fault' it is? Be the bigger man. Say 'I'm sorry you took my comments badly, that wasn't how I meant them. I love you, and you know that (assuming you do...) and I never meant to hurt you. I'm upset that you read my conversation because I expect to have my privacy and your trust.'
She might want to qualify a few things, or make a few requests. If you're not happy with those requests, make your reasons. Make your own requests (i.e. not reading your facebook). Relationships are about compromise. There are going to be misunderstandings and upsets, but the way to deal with them is not to place blame and get into a mentality of 'who's right'. At the end of the day she insulted your right to privacy, and you upset her with the way you spoke to a friend. Learn from it: when you speak to friends, think about what she'd like to hear. I'm not saying censor everything, because talking to friends can be a good way to let off steam, but think about how she might interpret what you're saying. And in turn she'll hopefully grow up enough to realise you have a right to keep things private and to talk to your friends without her witnessing it.