Science Fact: Women remember arguments better than men; both sexes remember different details about everyday things.
Explanation: Imagine a couple having a mundane argument. It should be based on something that's at least potentially forgettable; like, "Why don't you ever remember stuff about my interests," a disagreement that leaves no obvious physical evidence, as opposed to "Why did you flush my yappy dog, Mr. Jingles, down the toilet."
What happens in the aftermath of a fight like this is that a woman goes "Argh, boys," and actually remembers the words that were exchanged during it. She furthermore remembers the guy's demeanor, the subtext to the stuff he said, and whether or not Mr. Jingles was a lovable good dog or merely a horrible mangy idiot. When a guy has the same argument, he goes "Argh, I am angry!" and then destroys a fishbowl for some reason, and then has absolutely no memory of what this fight was about 24 hours later (or, occasionally, wakes up with no memory that there was a fight at all).
The Science: There's a lot of research on this. One scientist who wrote a book on this subject explains that, in an argument, women experience a burst of cortisol—the "oh nooo" hormone—that persists for the whole day. Guys also experience a surge of cortisol, but it subsides much faster once the argument is actually over. They get mad, but then that fades. They throw the TV in the garbage and tell the cat that it is a failure and then eventually forget that anything ever happened. The stress hormone that causes them to dwell on the context of a fight simply isn't there anymore.
But that's not the only memory quirk at work here; guys and girls actually remember the world differently, too. A Vanderbilt study showed men and women pictures of various objects—birds, cats, mushrooms, cars—and then showed them another series of similar pictures and asked them to pick out which specific pictures they'd seen previously. Guys recognized vehicles much better; girls recognized animals much better. And this quirk of memory isn't due to Male-Female Brain Weirdness, but simple conditioning; very generally, men know more about which is the raddest kind of motorcycle than they know about which is the best kind of owl. (For the record, the best kind of owl is obviously the white-faced scops owl.)
So What Should I Do About It?
This might all seem like a lot of simple observations, but there's a whole lot to take away from it. First, people literally remember the world differently based on their interests and abilities; nobody has the exact brain you have. A guy who has trouble telling your female friends apart, or a girl who has trouble telling your wonderful ponies apart, probably does not think that your friends are irrelevant, or your dumb magical ponies are for stupid babies. Other people simply lack the groundwork you have to differentiate the smaller details in these situations (unless they actually dedicate themselves to it, of course).
And on top of all that, we remember events differently, because for better or worse, men are less equipped to remember stressful arguments. There's a quote out there about never attributing something to malice when it can be explained by stupidity. Well in this case, never assume that a dude intentionally forgot an argument because he doesn't care about you, or that a girl keeps clinging to an argument because she's spoiling for a fight, when you can instead assume that our brains are pretty much designed to make us want to throw each other off a bridge, all of the time.