The most common argument against women warriors is that men are heavier and have more efficient muscles. Often, the existing differences are exaggerated to make the case stronger — for example, I heard one man insist that women had 30% of men’s muscular strength, when the usual figure in studies is around 70%. However, if you want a believable tough woman, that single statistic is far from a rebuttal. There are plenty of ways to have women warriors in your story without sacrificing plausibility.
To start with, that figure I quoted is a statistical average. Your character can always be an exception, like George R.R. Martin’s Brienne of Tarth, who is an unusually tall and stocky woman. Such a woman might have XXY chromosomes, or a high level of testosterone, but height and fitness might be all that is needed to account for her greater than usual strength. Nor is there any need to make her plain or give her body issues, the way that Martin does or to make assumptions about her sexual orientation– plenty of athletic women of all preferences have a traditionally feminine side.
Alternatively, you can take advantage of the fact that muscular strength is not the only factor that makes a fighter. In World War I, the English briefly raised Bantam Battalions, consisting of men under five feet two inches, who were considered too small for regular units. The Bantams consisted largely of miners and other hard laborers, whose lives had made them tough and fit. Some had the habit of successfully challenging ordinary sized men who under-estimated them. The Bantams did not last long because of the difficulty of finding enough recruits, but the fact that they were absorbed into regular units after being disbanded suggests that their ability to fight was not an issue. The example of the Bantams suggests that many women could also hold their own in combat without being unusually large.
So what other factors make a fighter? Training, speed, agility, endurance, and the ability to endure pain are at least equally important, especially in combination. In all these areas, women could equal or excel men. If you consider the rigors of childbirth, women might even be argued to be superior in endurance and withstanding pain. Moreover, if you have ever wrestled or fought in the Society for Creative Anachronism, you will also know that bluff and the willingness to fight are also important: quite simply, if you look or act fierce, then in many cases, you will have already defeated your opponent before the fight begins. A woman might also distract men by jeering at their machismo to give her an advantage.
Probably the most important consideration is tactics. The average person of either sex is not going to stand toe to toe with a 120 kilogram man for any length of time. That is why sports like wrestling or boxing are divided into weight categories — otherwise fights would not be fair. The smaller opponent would be battered to death. So, instead of a sword, your character might be better off carrying a spear or a halberd — anything that would keep superior strength at a distance. At all costs, they need to avoid a clinch, and keep moving. In general, time will be on the smaller person’s side, because they expend less energy in moving than someone taller and heavier, a fact that is reflected in the occasional calls for weight categories for marathons.
In general, I see two basic tactics: either hold back and take an opponent apart a piece at a time, or attack first, disconcerting the enemy, and getting in the first blow. What average women cannot do is fight on the enemy’s terms. They must fight on their own terms, and be smart about it.
However, in some senses, the argument against female fighters is moot. It focuses on hand to hand combat, which is only a part of warfare in many eras. In early or pre-gunpowder eras, what mattered was often the ability to remain in formation, which is entirely a matter of training. At the battle of Waterloo, for example, British regiments resisted charge after charge of cavalry by remaining in squares and holding off attacks with bayonets — and a horse is by far heavier than the biggest man, and neither cares to fling themselves on a length of steel. What matters is less physical strength thn holding the formation.
The counter-arguments also ignore irregular or light tactics, which can be as far from hand to hand combat as you can get while still be on the battlefield. Such troops skirmish, snipe, ambush, and, if mounted, scout. They also provide support for massed formations so that they can’t be out-flanked. Bernard Cornwell’s Sharpe books and TV episodes depicts them very accurately, and even acknowledge that the Spanish guerillas in the Peninsular War against Napoleon included women. In many ways, skirmishing is ideal for women, since their smaller average size might help them to take cover and move silently, and be less weight for a horse to carry over long distances. In fact, historically, light units were the opposite of the grenadiers, the heavy set shock troops, and were recruited for their intelligence and independence rather than brute strength.
If none of these suggestions are convincing to you, consider modern armies, where women often serve in support capacities. Being a clerk or cook might not sound exciting, but reversals of situations are common in a campaign, and someone who appears to be safely behind the lines can find themselves suddenly in the middle of the action, as happened during the Battle of the Bulge at the end of World War 2. Imagine, for example, a woman who is a quartermaster who suddenly finds herself the senior officer in her area. Or perhaps your character could be in charge of a seige engine or cannon behind the lines, and find herself facing a flanking attack.
So ignore the chauvunists who say women have no place in combat. You can have tough women if you want them, and still be believable. Just don’t make them exactly like the men of impoverished imaginations. And in doing so, you may discover new stories to be told.