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Bodyguard? What bodyguard? I see no bodyguard!

The king is the winner of an election-by-combat. It would be impolite to suggest that he needs a bodyguard. That would mean he is no longer fit to rule, after all. Even if everybody knows that the king is too old and fat to win such a fight today, everybody pretends otherwise. Anything else would be a grave insult.

The king can have senior military officers at his court, but if they follow him into his private quarters they will look like bodyguards. Can't have that. Likewise, he cannot arm his manservants. But what he can do is to arm his maidservants. They need a weapon to protect their virtue against those ruffian stable boys.

It would help a great deal if you could give us more information about this culture you're creating. Regardless, here's a handy list of reasons why women would be preferred:

Inheritance. Men in a king's security force might have some interest in becoming king themselves, or may work with another man who wants to become king in order to garner favor. Women, on the other hand, can't be king, and depending on how you arrange your setting they may be forbidden from holding much power at all. Being a king's guard may well be the highest office these women could hope to obtain.

Religion. Anytime you want a society to do something that would seem irrational to an outsider, religion is an easy go-to. Perhaps some ancient sage predicted that a male guard would turn against the king. Maybe this society worships a female goddess of war or protection.

We don't have the men! Maybe all the men are in the army or busy farming, and the women are the only ones who are willing to give up whatever they're engaged in in order to guard the king.

Superwomen. Perhaps a small percentage of women are magically blessed with ridiculous strength or speed. Maybe the bloodline of the Amazons of old runs through some women's veins, making them superior fighters.

That's a woman's job! Perhaps the act of guarding someone or something is considered dishonorable for men, and more in line with the role of a woman in keeping the hearth or some other cultural explanation.

We've always done it that way. The first king was guarded by a woman in his old age. Maybe it was because of one of the reasons above. Maybe she was just a particularly able fighter, or perhaps he only trusted her. The reason may be lost to time. Regardless, she ended up shaping the institution that became the all-female king's guard. Now it's just tradition.

Eye Candy

A lot of despots have really attractive female bodyguards. Really as far as safety goes, a man gets killed just as easily with a gun as a woman so the extra strength really counts for little. A woman can shoot back just well as a man so there really is little difference. Strength matters if it comes to hand to hand fighting but since the invention of guns, it makes no difference.

What you are left with is body guards that are easy on the eye.

It's the same reason why it was a mark of prestige for the German generals and other high ranking officials to have a female chauffeur during WW2.

Yes this is a sexist thing to say but a lot of male leaders are sexist pigs. Female bodyguards are a mark of power and prestige and it simply wouldn't do to have males one. That would make you look weak.

Witches.

I am starting to wrap my head around your world, Incognito. If this is the same world your other questions come from, there exist witches and the witches are always women. Witches have magic, and especially working in a team are more powerful than any group of men could hope to be.

The answers are many, but I notice a few things which can be woven together.

The first is that the king may have written these women into place. You don't mention why men are forbidden from being body guards. However, it could naturally come from fear. The king might fear their bodyguards being too dangerous and too close. This could lead to a cadre of women surrounding the king, which might play out like Quadafii's example. However, what if they got good at hiding their skill? What if they learned to be deadly in a way the king did not recognize. This would mean the women have learned a skill which the other men did not. If you try to be as deadly as them in a "male" way, the king recognizes it, and kills you. Be deadly in a less familiar way, and the king may simply not notice.

And, of course, women have quite a head start on a "less familiar way." Whenever I play with gender stereotypes (which gets more dangerous every year), I start from the assumption that the primary effect of gender stereotyping is that each gender gets a head start learning a set of skills that are enormously difficult to learn if you don't develop them during childhood. Skills such as fighting are taught based on assumptions of these skills. We teach the military the way we teach the military because it is effective for teaching men how to fight, based on the skills they learned up through high school. Modern militaries are still in the process of figuring out what it looks like to teach to both sexes and/or genders (I'm not entirely sure which the military teaches to).

This creates an interesting niche for your women to sustain their position. If they develop a training regimen which is effective for teaching women to fight based on the skills they have developed as a child, that training will be unavailable to men as long as the society is gender divided enough to prevent a large number of men from learning the skills typically learned by women. These women fighters may retain their position as "the best" because there simply is no training regimen available to make a masculine individual that deadly. (which would also lead to a whole host of interesting side-stories as those who do not fit perfectly into these neat little gender bins might be able to pick these fighting arts up successfully, creating all sorts of fun complications!)

This may also result in interesting skewing of "traditional" gender roles, as men adapt to this deadly art. How those gender roles skew is really up to you, and what gender story you wish to convey.

What your question is grappling with is a biased idea that men are better than women. There is some anatomical difference, but in a technological society, those difference are easily overcome.

When coupled with any tools, technological advantage and training, the physiological difference of an all male group and an all woman group is moot. Take an example of a unit of longbowmen. The difference in capabilities between what a man can do verses what a woman can do is they little. As long as they can pull the bow string, they both can kill over the same distance.

Can be as simple as a layman male with a knife verses the highly trained woman with a sword, the king would be protected any day against this threat.

To answer this question, all your society needs to overcome differences in the gender make up of said units is to overcome their bigoted and chauvinistic way of thinking.

In human history a male ruler might have a harem of wives and concubines. These were confined to a closed-off part of the palace that could be accessed only by the ruler and castrated male servants and guards.

Female guards would be the ideal way of working this without resorting to the unkindest cut of all.

Actually, I don't entirely agree with your premise that men are 'stronger, bigger and faster' than women, but even if we take the first two as a given the faster is subject to some interpretation and I'd argue that there are two crucial areas where women guards would be superior to men;

1) Flexibility

Men may be faster on average in a straight line race (according to Olympic records at least) but that's not the only definition of 'fast'. Women, in my experience, tend to be more flexible than men, and more agile. In the cut and thrust (no pun intended) of close quarters protection detail, quick reaction speeds tend to be more important. Being able to be 'where the enemy is not' in terms of spears, knives and even guns is an important part of such combat, and the ability to throw oneself in the path of a bullet after only just noticing the threat is going to be more the domain of someone nimble, agile and flexible, which to me sounds more like a fit woman than a strong man.

2) Multitasking

Yes, it's a stereotype, but again in my experience women deal with chaotic environments better than men. In an environment where potential threats are everywhere, I suspect that women would actually be better at tracking multiple threats, meaning that they have a good chance of identifying an actual threat from many sources, whereas a man generally has a great chance of identifying an actual threat from one, maybe two sources. That means that you don't need a small army tracking many different potential threats in a crowd via surveillance; you have a team of women on the ground that can do almost as good a job as your small army of surveillers at identifying when a suspect becomes a real threat.

I don't like these kinds of stereotypical comparisons between genders because I'm not a fan of people getting jobs because 'men are better at...' or 'women are better at...' and I think that if you really want to protect your king, you need a balance of skills that are sourced from the best pool of 'people' you can gather. I'm a firm believer in the best person for a job, but even I have to admit I live in a world where the prejudice exists both for and against men, for and against women. That said, if your female protection detail formed from convention, I can imagine this might be the reason why it started.

A deterrent. Men are less inclined to kill women than they are men. Female ninja or whatever you may call them would even bare their breasts when they were discovered as they would stand a larger chance of getting captured rather than killed when they did. But this is a small deterrent against someone willing to kill the King.

Social and cultural cunning.

Women are on average more adept at social and cultural situations. From being able to recognize faster who's head is who's based on clothingstyles (https://images.app.goo.gl/1mp3h2omLvJCJgZq6) to a better understanding of people's behaviour or cultural background. This is one reason why female normal functioning autists are much harder to detect than male one's, as the women get bombarded with social input and necessities much more frequently as they grow up than men and subsequently seem more natural at it.

The consequence is that the female bodyguards are better at determining a threat before the attempt at the King is made. From just filtering bashfulness in front of the King and edgyness before a strike to being able to recognize a clothingchoice or cultural difference that might signal a potential threat. It doesnt matter how strong, fast or big a bodyguard is if he cant detect a threat in time!