A Star Trek: TNG episode titled, Angel One is an example of the type of episode that struggles with a moral and social dilemma. Characteristic of this type it is suspense driven, with characters facing grave danger (which is an excellent tool too enhance your sense of moral outrage); in this case a sentence of death awaits merchant spacers and the indigenous woman of a matriarchal regime with whom they fall in love.
From ST:TNG’s first season it stars Patricia McPherson of Knight Rider, and I believe a member of the 1988 Men’s Gymnastic Team; as a member of that elite and a spouse of the same, any fan will find the story intriguing. However, in classic Roddenberry tradition it is episodic. The problems must be solved in an hour (or brought to life in the least, so the locals can work it out) and then they move on to the next adventure. This naturally leaves little time for worldbuilding, of the stem culture (i.e. the Federation) much less those that they come in contact with.
This is a perfect example of a culture that could be expanded. First, what could have led to a society where human or humanoid females are dominant? The answer would certainly have to be biological, although not necessarily physical. Suppose, that these females had the ability to emit pheromones at a level that amounted to mind control (fine tuning hormone levels to command specific responses with the aid of only the most basic verbal cues). This alone might suffice, but also imagine the capability for reproductive control, such as voluntary miscarriages and organic or artificial embryonic and fetal transfer.
What sort of society does this lead to? In the case of reproductive control, natural reproductive control would require us to rework the alien species from the very human aliens in the episode. Does the production of the male sex cell require the ingestion of food that lead to small bodies, yet are agile and active to chase their fleet prey and perchance the female diet consists of large and dangerous catch necessitating a need to control one’s reproductive cycle to maximize the numbers in a hunting party and leading possibly to a neuter gender for child care (John Dalmas’s Soldiers envisions such a species as does TNG in a later season). Also the ability to control the males in such a threat heavy environment will enhance species survival.
If this were to be done artificially, then would we be looking at mechanical devices, chemical and genetic alteration or some combination of all three. Political upheaval could lead to this, especially if a repressive patriarchy were overthrown. It may be accomplished by a drug regime given to key and influential figures to control them. Women may start taking advantage of and increase research strenuously in the area of reproductive health to close the career gap, that child rearing inevitably leads to. They may also see fit to genetically or mechanically engineer caretakers to free themselves up to rule.
Watch the episode and give the old mental muscles a stretch would you. Until then see you out there.