At least this situation has led to some excellent writing. Will, for instance has a better grasp of the gender-as-social-construct thing than I do.
To say that something is socially constructed means that its existence is dependent upon social relations and the contingent meanings that we create. In other words, we construct it and give it meaning through our social actions. That something is socially constructed does not mean that it is “not real,” but rather that it is depends on social relations for its existence. There are plenty of things that are socially constructed that people consider to be real without questioning it such as money, marriage, national borders, and even language. Similarly, gender (and race and class) are social constructions—their existence arises out of and depends on social relations.
He adds a lot more, all of which is worth a read.