While there are some notable exceptions, the vast majority of women in medieval and early modern Europe who came into combat situations did so in two ways: as occupants in towns under siege, and as camp followers of an army when the army's 'baggage train' was attacked by enemy forces.

As far as sieges went, frequently the besieging army would offer women and children the chance to leave the town initially. If the women stayed, however, they could count on being treated as enemy combatants if the town fell. We know many women did stay and fight. The legendary woman known as "Geische Marburg" who helped defend Braunschweig in 1615, for example, was used throughout the century (namely, in the Thirty Years' War) to encourage women to stay and help shore up defenses so their husbands could do the actual fighting. Jeanne Laisne earned the nickname "Jeanne Hachette" defending Beauvais in 1472 and today has merited a statue in the town. "Fiery Joanna" of Flanders (Jeanne la Flamme) led the defense of her town in 1342 and then led some of its residents to burn down the besiegers' camp.

The primary motive for these women was obviously to defend their homes! However, they certainly faced a double danger. Chronicles tell us of individual cases where women living in homes forced to host besieging soldiers had to flee to caves to avoid 'unwanted attention' (sexual advances, threat of rape). I imagine that women in a town suddenly under siege would have quite reasonably feared some kind of assault--sexual or simply mugging for whatever property they took with them--if they fled the city with their children. On the other hand, women who did stay behind and fight could be and were raped or killed in many cases if the city fell. So there is a potential sexual violence link in these cases, although it is somewhat the opposite of rape=>fighting, more like, hopeful avoidance of rape=>fighting.

As to camp followers. Medieval and early modern armies did not travel alone; they were followed by large amounts of support. Women in the baggage train tended to be of two kinds: prostitutes and wives of soldiers (responsible for food foraging, laundry, repairing torn clothes and scrounging new ones when the old ones were finally done for). These are not necessarily women who chose to become soldiers, but they knew the potential for them to be drawn into fighting if attacked was always present.

I don't think we can draw a rape=>fighting link here, either. Prostitutes (who were surely no strangers to sexual violence then--Karras calls her study of prostitution Common Women based on a contemporary term, as prostitutes were considered the common property of men. Right.) saw desperate opportunity. Wives came to help their husbands. There is certainly sex and rape in these camps; female camp followers in the Crusades reportedly died at a much higher rate than their male counterparts (among the camp followers, setting aside soldiers), and it's not hard to see sexually transmitted diseases as part of the reason. But this is still not a rape=>warrior tie.

Stepping outside history for a brief moment: The prevalence of 'rape as tragic backstory' and 'rape justifies vengeful violence' tropes in literature shows, I think, the power of our social ideas tied into rape (gender power imbalances, honor, shame, property, inheritance) and a certain lingering level of discomfort with women exercising violence, a need to justify it. For example. Tacitus tells us Boudica was flogged and her daughters were raped; men's lands were seized. Then Boudica leads the rebellion. Cassius Dio tells us only that Boudica was the wife of the former ruler, who leads the rebellion. Do the two stories present different pictures of her? Which version is true?

It's crucial to tread very carefully when trying to assign motives to historical warrior women whose stories we will never know firsthand--out of respect for women who have and who haven't been raped, who have one or who have many motives for fighting.

I'm going to supplement /u/sunagainstgold's answer with something from a modern era and I'm going to speak about something that is one of the core characteristics of modern guerrilla warfare: political ideology.

When French officers encountered captured, killed or just the concept of a female FLN (Front de libération nationale) soldier, they never tied their membership in an armed insurgency to political ideology or revolutionary thought. The idea of these urban young women, often seen as de-islamicized and 'western' than their male counterpart since they dressed in European fashion and looked 'white' or the rural young women, very much seen in the traditional stereotype of a docile and submissive Muslim woman, was that they never broke out of their established gender, racial and religious stereotype. If they were involved in the insurgency, against all odds in the French mind, then it was for a reason besides politics. Why women would be involved in the war to begin with puzzled the French officers, who sometimes grasped for straws in trying to explain the reason. Take this extract from the writings of Colonel Yves Godard of his encounter with Zohra Drif after she was captured during the battle of Algiers (1957):

"Zohra is a little woman, rather pretty but above all intelligent, marked by French education and culture. She dresses in the European style, and, with her chestnut brown hair that betrays a Berber ancestry, she can pass for a colonist’s daughter. That’s what she’s aiming for, moreover, but at the university there are idiots who remind her that she is called Zohra. So she starts to show an interest in those we call outlaws."

Godard comes to the conclusion that the reason for her joining the FLN was because she was teased for her Muslim name. That is quite a big jump to make from being supposedly teased by your fellow university classmates about your Muslim name to placing a time-detonated bomb in a milk bar frequently attended to by women and children, killing innocent civilians.

What actually motived young women to join the FLN was political ideology, the liberation and anti-colonialist ideology that the FLN proudly displayed. Women came to their own conclusions about French colonization and Algerian politics through their own studies or through being exposed to it at home. They had their own agenda as opposed to joining the insurgency because their husband, father or son did. Women came to use these stereotypes against those who believed in them, in particular their French opponents, and could easily slip through security checkpoints in Algiers for example.

Yet it is wrong to think of the FLN as an open-minded organization which allowed women without any issues. While the FLN ideology wasn't Islamic, the Islamic religion did have an impact on how women were considered in this context. The FLN preferred a more conservative role for women, as mothers and wives at home for their men as opposed to frontline soldiers, practically minimizing the women into the preferred stereotype of the FLN - very much like the French. Women were preferred to have more traditional roles, such as nurses, doctors or messengers, instead of being armed combatants. There were even official FLN orders forbidding women to be armed fighters but due to the autonomous nature of the wilaya (the administrative sectors in which Algeria was divided by FLN, led by their own military leaders), some women still fought on the frontlines while others did not.

A total of 1,744 women came to serve in the armed wing of the FLN in various positions according to post-war statistics from the Algerian government. They fought alongside men, and suffered alongside them. Some of them even managed to give birth to children during these difficult times and still being able to continue the fight against the French forces. These female insurgents came to play a very important role in the war and performed some of the most effective and iconic attacks of the war, despite the fact that both their opponents and their own leaders found it bizarre and downright unacceptable that they would. Yet their presence had an effect amongst their male counterparts that sometimes led to surprising results, as an Algerian nurse said after the war:

"There were many people [men] who took to the maquis when they saw these photos [of women in FLN uniforms]. They said, how can women fight while we, like 'women,' stay at home?"

Sources:

Algeria: France's Undeclared War by Martin Evans (Oxford University Press, 2012)

Transgressing Boundaries: Gender, Race, Religion, and “Françaises Musulmanes” during the Algerian War of Independence by Natalya Vince in French Historical Studies, 3:33 (2010), 445-474.

Well, there was Joan d'Arc, as the most famous general example. A quick search also discusses Matilda of Canossa, and wikipedia has so many examples in "Women in Post-Classical Warfare" https://en.wikipedia.org/wiki/Women_in_post-classical_warfare that I could get lost for days checking their sources. Good place to start looking for motivations, though; a quick glance seems to indicate religious conviction and perceived oppression coupled with some form of opportunity (inherited nobility, support rallied from others) as the most common set of circumstances.

Human nature hasn't changed all that much over the generations, though. As a woman who joined the military in today's society, I can assure you that today, women who engage in military activities have as many reasons for engaging in those activities as there are women to have an opinion. However - today's society offers a great many more opportunities for women to act in support of military actions than previous societies did.

While opportunities may have changed, you can expect women in previous societies to have held a diverse range of attitudes and opinions in their society; certainly moreso than modern media tends to portray, since the folks shaping common perceptions of women in history don't often get even the men's side right and that's the side that more frequently has more documentation to pull from.

You can get a lot of post-event analysis from guys discussing women's motivations in history, but not, in general, a ton of firsthand accounts from medieval times. Due to the general lack of modern interview-style documentation on motivations, if you want something more immediate than political analysis - you might try looking at more modern examples to get a good idea of the mindset of someone getting into combat from a female perspective. It's extrapolation but like I said - human nature is pretty similar, even when contexts change. And some of the societies women get into combat from are less altered than others, from their older forefathers.

If you're looking for an interesting older book on modern-ish women in combat - in this case, female terrorists - you might try "Shoot the Women First" by Eileen MacDonald as long as you recognize that she has a serious bias. She does manage to get some very interesting interviews and some good psychology of the women she profiles on the page, possibly because her approach to them is so flattering that she was given more access than might otherwise be seen. Her basic conclusions are that the reasons vary. Some examples are that women engaged in these activities because it provided them with respect which they couldn't get in their traditional roles, because they loved a man who was engaged in these activities, because they started out supporting a man but became genuinely devoted to the cause and eventually ditched the guy because he wasn't devoted enough, because someone's threatening their family. Mostly, sexual violence doesn't enter into her particular character studies except in the "gets more respect" arena.

What you have to recognize is that women, in the end, are human. We have the usual human motivations usually ascribed to men in popular culture - loyalty to a cause, pursuit of justice, devotion to country, anger at perceived unfairness, etc - just less of an opportunity, historically, to exercise military solutions to those feelings. Men have as much devotion to hearth and home as women do, even if they've had less opportunity to exercise it and more of a traditional social responsibility to the military. You'd find men in the Army who wanted to be there and men who didn't, with varying levels of skill and intelligence. It's not a cohesive whole by any stretch. Some might go for the money and some for the glory and some for the adventure and some for escape; no one answer will ever be true for everyone. Given the opportunity to do something, a certain percentage of women and men will retreat, and a certain percentage will attack.

The one thing I'm not seeing in these historical examples is "personal rape as motivation" from a source close in time to the event. Rape was and still is extremely common in wartime. It's also not something that tends to make women - or men - feel empowered and strong enough to do anything about it, which is, as far as I can tell, somewhat of the point of the act in the first place.