Haven't written one of this series in a while, so here goes:
Men and women often employ completely different styles of argument, which bear scant resemblance to each other.
Women have a tendency to turn all arguments personal. Argue about any subject under the sun, and women will find a way to make the argument about you. (If you then defend yourself, the dumb ones will give you a look of disdain and say, "It's not all about you, you know.")
Men, in turn, will threaten physical violence -- not necessarily overtly, but with their body language. They will get in your face, ball up their fists, stick out their jaws, and maybe even do a mini-lunging move at you.
If you outargue a woman, and she has no facts to back up her case, she will simply change the subject. If you try to keep her on topic, she will resort to, "I don't want to talk about this anymore," or "Life's too short to argue about things like this," even if she's the one who brought up the topic and started the argument.
Or, she might say, "You always have to be right, don't you," turning the focus back on you -- as if the entire argument has been nothing but a display of your faulty character.
When an argument gets heated, men will stand closer and get into a fighting stance and show their teeth and jab their finger towards you. If they're angry, the veins in their neck show; if they're really angry, the veins in their forehead show.
A woman will roll her eyeballs and shake her head, or make disgusted little noises in her throat or with her lips. ("Kkkkuhhh," or "ppfff.")
If women are angry with you for one thing, they will often pick a fight about something else. For instance, if you were being friendly with another woman, they might get really nasty about how you didn't help enough with the cleanup.
Men tend to be more direct.
Women are more likely to try to win an argument by setting up straw men. If you're arguing about general tendencies, they'll say, "Oh, so that NEVER happens," or, "Oh, so NOBODY EVER does that," as if you'd been talking in absolutes. Some of them seem to think that one exception proves a stereotype can't have any validity.
Men are more likely to use mocking humor. They are more likely to take your argument and apply it to another situation to show how wrongheaded it is.
Women are more likely to try to put words in your mouth, and claim that you've said things you haven't said.
Men are more likely to try to imply that anyone taking your side in an argument must be lacking in masculinity.
If the argument is about a third person, men will often talk about exactly what sorts of violence they'd like to do to that person, in suitably colorful language. (You almost never hear this from women.)
If a woman decides to insult you, she will do so in a very personal manner, picking whatever it is that she thinks will be most stinging to you. (Should you do the same to her, this merely proves that you are evil.)
A man will use more colorful language, but generally doesn't get as personal. ("Fucking asshole" is strong language, but it doesn't really have any personal content.)
Boneheads of both genders will say, "Oh, well you were the one who said...." as if having made one past mistake disqualifies you from all future arguments -- and as if they've never made a mistake themselves.
Boneheads of both genders also tend not to listen to what you've said, and to just repeat themselves over and over.
In past posts on gender differences, I've tried to be evenhanded, but all in all, I have to say, I usually prefer arguing with guys. (And no, I am not positing the tendencies above as absolutes: there are men who get bitchy, and there are women who try to appear threatening; but the general correlations hold.)