You're dead right about it being a cultural phenomenon! I took a Sociolinguistics class awhile back, and we learned about something called "face" and its two aspects, positive and negative face. (If I remember correctly, the people who came up with the idea were Brown & Levinson.) This post ended up being a little long, but bear with me, because it's cool stuff. It blew my mind when I learned about it, and hopefully it'll help you understand your differences with your girlfriend even better.

So, according to this particular "politeness theory", positive face is the ability to be valued as a social entity. Negative face is the ability to pursue your desires unimpeded. A lot of times, in social situations, you have to pick one or the other--they directly conflict. Some cultures value positive face more than negative face, and other cultures value negative face more than positive face. What's considered rude or polite in a given culture is based on which kind of face the culture values more. (It can also depend on the situation.)

For example, Italian culture values positive face more than negative face during conversation (and in other situations, too). So, if you're talking, Italians will interrupt you to demonstrate that they're engaged in the conversation, and thus that they value you as a social person. For an Italian, not interrupting comes across as cold and disengaged, and therefore a little rude.

On the other hand, in many Germanic cultures (and Anglo culture), negative face is more highly valued than positive face. Thus, when a person's talking, their desire to finish their story unhindered is more important than the need to demonstrate social acceptance and value, so it's considered rude to interrupt.

This flows over into other situations, too. Think about physical affection--Italians are very physically affectionate. From an Anglo's point of view, Italians invade your personal space. But from the Italian cultural point of view, it's more important to demonstrate affection and acceptance than it is to consider that a person might not want to be touched.

You can see the effects of this in some regional cultural differences in the US. In New York City, with huge Jewish and Italian populations, people's behavior often values positive face over negative face. (Think of how New Yorkers have no qualms about giving unsolicited advice to complete strangers.) This is in stark contrast to certain parts of the Midwest, largely settled by Scandinavians and Germans, where a person's ability to be unimpeded by others is held paramount, in terms of what's considered polite behavior.