Not because they can't perform military tasks, but moreover because they are the only hope for continuing a civilization. The notion of not allowing women to participate in battle was never originally intended to be demeaning towards women, it was mainly just for the protection of a species. Don't send the child-bearers into a situation where they would potentially die, that's a great way to get wiped out. Over time though, I can see how that evolved into a very demeaning perspective of "you're just a woman, you can't fight." So in times like this, where the population is thriving, women should absolutely be able to do what they want. If in a time of extreme warfare, our population ever starts to diminish, I think that women should be a protected and vital element to preserving the species.
Men are naturally stronger than women. In the military, physical strength and endurance can play a major role not only in a soldier's survival, but also in the success of a battle. Technological advances have taken much of the fighting away from the front, but human forces on the ground must still rely on physical capabilities to succeed. With such high risks on the battlefield, it is in everyone's best interests if the military is male-only.
Fighting in the military involves strength and skill. Women who meet the criteria to fight in the military should be allowed to do so. That being said, the requirements, both physical and mental, to work in the military should not be relaxed for women; they should be held to the same standards as men.
Some studies have found that mixed squads generally have better behavior than non mixed squads. Also women do excel in certain roles do to their biology, one example being counter sniping thanks to their smaller figure. In the end however, whether someone will make it in a particular role is up to the individual. A persons gender is not so restricting as to literally make it impossible to do most tasks required in the military.
The United States maintains a military that is made up of all volunteers. That means that all citizens who are eligible should be allowed to apply to join the military branch of their choice. However, all people who are accepted into the military should have to meet the same minimum, uniform standards.
The idea that women cannot be productive members of the military is sexist. Women have repeatedly shown themselves to make just as strong military personnel as men. The traditional belief that women need protection does not really have a place in contemporary society and the idea that women should be kept out of the military is nothing more than a remnant of that mindset.