But, of course, there were cases when women fought in open battles – I myself remembered something and posted it in the first post on this topic.
As for belittling men's achievements – that's definitely not the case, because for a medieval person:
firstly, a man was clearly so much higher than a woman that such cases wouldn't belittle him;
secondly, the motif of a female warrior is quite popular in various legends (and, by the way, it is presented there as something amazing! The only exception – and I also wrote about this – is Celtic mythology), and therefore, it attracted men's attention.
As for combat training for women... I don't know, Archer, where you got this from, but I, and for example, Marc Bloch, and countless other historians (well, I'm not a historian, of course:D), share the opinion that in the early Middle Ages, in its heyday, and in the late Middle Ages, women were only taught to manage a household. They even started teaching them to read and write much later than men. And there were no female alchemists (that's a fact!), and they didn't study at universities (but now we have only girls in psychology:D).
And as for Europe, you're exaggerating. In Europe, women were always treated with much more respect than in China or Arab countries – it is enough to say that polygamy appeared in China (although, perhaps, it actually appeared even earlier, in the Paleolithic era), and in Arab countries, a woman is almost not considered a person (and how else to explain the fact that paradise in the Quran is described only for men? As far as I know, nothing is said there about what may happen to a woman after death). Women were most respected in Western Europe (chivalrous gallantry:)), and they had the most equal relationships with men among the Vikings – they asked women for consent to marry, they could insist on a divorce, and in general – read the sagas and you will see for yourself:)
Added 1 minute ago
Yes, and one more thing. I think we've gone completely off-topic about female warriors:( Let's either open a new topic to discuss this issue, or just move on to elves. At worst, to elven women;)