You're not old fashioned, you're "new fashioned," imo. In the past, when marriage was held in higher regard, there was considerable pressure on men to propose not only to obtain sex, but to ensure that the woman would not be snapped up by another man. Women had any number of what they called "callers," or "beaus." Engagement was the only thing that ensured any degree of monogamy. But now all dating relationships seem to be considered potentially matrimonial relationships. In my opinion, it's unfair to people, ridiculous, and the cause of the high divorce rate, as people don't have any opportunity to meet "the one."
I'm very serious about this. The "grey area" I refer to isn't a matter of communication at all; it's the idea that once you start seeing someone, there's some assumption of exclusivity, for some reason. Why should there be? If you're dating, you're dating, and that's that. You're not married. It bothers me when I see wonderful men hang back, afraid to ask out a girl because she's "seeing someone." So what? Ask her out. She's not married; she's as free as the wind.
Incidentally, no one can "break up" a relationship. People make choices. Everyone is responsible for their own choices.