From the my stand point there's three reasons why I don't argue with women, and probably never will:
Sex
Food
Courtesy
Now the first reason is pretty simple, she'll hold out on sex. As awful as it sounds that is actually a huge punishment. The second reason is a bit different, but really who wants to eat alone? Also of note is that I'm an awful cook and nobody goes to a restaurant by themselves. The third reason is a personal philosophy. There is absolutely no need to argue with somebody important to you. It won't just hurt them it will also hurt you.
Now none of these apply to strangers. But why would you argue with a random stranger?