Should Women Soldiers Be Assigned to Combat?

During the Iraq war, an Army medic ran through gunfire to rescue wounded comrades, earning a Silver Star. But one rescued man said she should never even have been there. The medic was a woman, even though women are never assigned to combat. They're getting closer and closer, and there's a budding movement to make them eligible for all things men do, if they can meet the qualifying standards. But that's hugely controversial.  Is it just about equality under the law?  Is it a cultural issue, deeply ingrained despite the guarantees of the Constitution?