I think it's worth discussing the context of this comment a bit.
Roddenberry's original vision of shipboard life in space was based highly on shipboard life in the US Navy, and particularly the submarine service. This is a pretty good model, because you have the somewhat contradictory social pressures of a military structure that must maintain good order to function properly, while also being a relatively small group of people sharing a confined living space for extended periods of time. You can't really escape from each other. Also your living space is a fragile piece of equipment that you have to maintain carefully in order to stay alive, the only thing between you and the hostile environment outside.
In 1948 the Women's Armed Services Integration Act was passed, which:
enabled women to serve as permanent, regular members of the armed forces in the Army, Navy, Marine Corps, and the recently formed Air Force. Prior to this act, women, with the exception of nurses, served in the military only in times of war.
However:
Section 502 of the act limited service of women by excluding them from aircraft and vessels of the Navy that might engage in combat.
Fighting was a job for men, you see. The definition of "vessels that might engage in combat" basically covered everything the Navy had in service, because even a support ship might have to defend itself from attack.
As a result, there were no women serving on the bridges of any Navy vessels.
This finally changed in 1978 in Owens v. Brown, in which Judge Sirica declared the prohibition of shipboard service for women to be unconstitutional. At this point women began serving aboard support and noncombat vessels. Congress finally approved service for women aboard combat vessels in 1993.
Women were still prohibited from the submarine service until 2010.
When The Cage was filmed in 1964, the idea of women serving on the bridge of any vessel was 14 years ahead of its time, and if we consider that the USS Enterprise was a ship-of-the-line, a true Starfleet combat vessel even if her primary duty was exploration, then 29 years ahead of its time.
Taken out of context the original line seems sexist and repressive, but in its time it was projecting a very progressive view of uniformed service.