Security ... think about it!
Serving with about 140 men, confined inside a submerged vessel for extended periods of time, is quite an experience. There are things that are said and that take place on board that would not be compatible with women. There are times when you have weapons drills at all hours and are barely able to make it to your duty station fully clothed, sometimes in just your underwear. I can just imagine a woman trying to get to her station, trying to get dressed on the run with men gawking. I cannot imagine women being on a Trident submarine submerged for 60 to 70 days, living in close quarters with men. I don't care who they are.