It's an attempt to make you beholden to her for any- and everything you will ever do, say, think or feel for the rest of your life! Now, combine this fact with the fact that you had no agreement (only an assumption on your part) to be monogamous in the first place! If you don't extract this agreement right now, you're never going to get it.
Further, it's always going to be an issue in your relationship from this point on, so get it handled.
Just last month, I met a cute guy and we went out and had so much fun together. Now it’s been a month and we’ve gone out four times.
The last time I saw him, I asked him if we could define our relationship. I decided that everything was probably okay until yesterday when my brother went to a coffee shop and saw him with another girl.
You should also do one more thing - you should discuss other aspects of your relationship at the same time. " Believe me, she's going to give you a laundry list of things she expects like, regular dates, being nice to her mother, etc., etc. Here's what I expect of you: ..." You can now get YOUR expectations met!
Well, about a week ago I had a one-night stand with a different girl that I met at a club. Now, I think she is going to give me a second chance. The very first thing you need to do is to stop apologizing!! Just as you've mentioned, you don't have any agreements with her about being exclusive - and after just 2 months of dating, I don't why you should have such an agreement anyway. You're taking the feminine view of your relationship with her and that is never a good thing!
I have been seeing this girl for about two months and never said anything about being exclusive.
What about picking you up from the airport when he promised? Of course, these same women "trust" their guys to do these things, so the fact is, there is a "level of trust" involved. Then, you need to say, "What I'm hearing from all of this is that you want an exclusive relationship with me.
In other words, to simply say she doesn't "trust" you anymore is a cop-out. From this point on, I'm willing to give that to you but only if you'll agree to do the same thing for me." If she agrees, you've got a new, fresh start but, make her agree that she isn't going to throw this back in your face later!