Considering the "militia" is essentially every able bodied adult, and the point of the militia is to defend from foreign and domestic threats alongside the military, it's not unreasonable to assume that men and women should have access to the same weaponry commonly fielded by our troops.
As for pitbulls, do I think people should have the right to own them? Yes, but not under the 2nd amendment.
Remember, not every "right" of the people is spelled out in the Constitution. It was never meant to specify every right. The rights listed in the Constitution are redundant, they shouldn't even have to be listed. Many of our founders feared that the creation of a BoR's would mean that those would eventually become our ONLY rights...