It's not impossible to imagine that at some point before TOS a number of female starship captains started going mad and neuroscientists claimed to have found some facet of female brain structure that made women peculiarly susceptible to madness under the combined effects of deep space and the strain of command. (And maybe Number One was... different, of course.) In an abundance of caution, Starfleet made the controversial decision to exclude women from starship command (with which Kirk did not agree).
By the time of The Wrath of Khan, they had a pill for it.
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you could perhaps read "Your world of starship captains doesn't admit women" to mean Kirk couldn't serve on the same ship with someone he was in a committed relationship with. (After all, they'd have to be on the same ship to roam among the stars and kill each other, wouldn't they?) This would dovetail with Kirk's "no beach to walk on" soliloquy about the loneliness of command in "The Naked Time"; as captain, he's married to the ship.
In her psychotic state, Janice wants to take revenge on Kirk and his world of starship captains, not just by becoming a captain, but by becoming him.