Ugh...have to start with the obvious: your thread title is vague as hell (hint: if you won't mention your topic, it'll be seen for the clickbait that it is), and the video is typical AI slop. I bet that you've got multiple similar ones in your youtube feed, with same formatting and perhaps even the very same AI voice-over. Seeing how your part about Tay-kwon-do has nothing to do with the classroom setting (only watched about half to get the general idea), I take it you're triggered into your own memory rather than want to discuss the video.
And that's okay. My view on the gender war is nuanced, but if it has to be black and white,I'd rather be in team "feminism is bad" than "feminism is good". Here's my own sob story:
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Let's see...I was part of a BDSM movement before metoo, and even before 50 shades became a thing. What I found was, rather ironically, a place that valued consent way more than elsewhere. Probably exactly because we engage in scripts and actions that can be seen as violent or abusive, it's extremely important to check with one another that the actions we do are absolutely, 100% agreed on by both parties.
It's also the reason I still have a (signed) list of the kinks of an ex-partner of mine. Because she was (and for all I know: still is) a predator. Absolutely not in the traditional sense, but it irks me that her behavior barely has a name, let alone it being recognized as a possible danger. Simply put: she wanted someone to birth her a baby and pay for said baby. At least: that's my take (she never SAID so, only ACTED exactly as such). For all the idea of her wanting to be my slave and such meant absolutely nothing. She got pregnant while we were dating, but when I took things seriously and made plans to move in together, look into daycare centers and such, she just delayed and sabotaged all my efforts. Even broke up with me. That's when the fighting started, as I told her it's her life and her consequences.
The BDSM part and their consent-mentality isn't a mere detail: because everyone knew me, the people she then tried to turn against me all sided with me. It's only because her plan to shame me into paying for her plan failed so spectacularly that she ended up getting an abortion.And blaming me (as if that was my intention somehow).
She got the same respons from my parents, who initially were open and welcome, but tabbed out when she took the initially offered help with the baby to continue after she broke up with me.
The thing is: I never really cared that much about all this gender stuff up to this point. I realise that I've been accidentally VERY LUCKY on both my social and familiar life. This woman that I've only known for about ten months total (half of which was this drama soap serie) very well had the potential to ruin my social and family life that I had built and maintained for the (then) thirty years prior. If she had played it smarter, or if I had taken a less disarming stance (I honestly WANTED to build a life with her and our baby. Just not as her ATM) things would've been different. Perhaps it also would've been different in my disadvantage if I had a job back then (alimentation isn't exactly much if I had no job and she did).
And now? I've got no doubt that feminism rightfully started as a means of more equality and a safer position for women. But while I feel that goal is, on average, reached, it also opened the door for women who see the gains as a means to a comfortable life of tricking someone or getting a professional carreer not on their own merit.
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Now...with that all out of the way, I've got to tackle the actual topic you want to talk about: the gender impact on martial arts. I should say "I disagree", but do note that we each have our own perspective, our own experience and our own sports in our own countries. This isn't an attack on you but rather a nuance that it's not everywhere like that.
I practice karate. For...fourteen years now, I think. The very gender thing I've learned exists in the world (see spoiler text above) simply doesn't exist in the dojo's I know. My current club is about 30-40% women, and about 20-30% in the club I previously visited. They follow the same training, given the same practices, everyone spars with everyone (okay: in a large group divided by belt level...usually), gives the same respect to one another. Just toilet and dressing rooms are separated.
Given the sport, I've got two anekdotes that are very similar. In fact, the act was the same: I had a female sparring partner, found an opening but miscalculated, and hit my partner on the boob. This is where the stories diverge.
More recent: she called me out on it. I immediately step back, stop the excercise, apologise and asks if she's okay. She is. Somewhat more carefully, we proceed. Done. This was about three weeks ago, and I had almost forgotten about it.
The older example happened very near the end of an excercise. I hit her, she looks startled but says nothing. I'm convinced I hit her below the boob, so have no idea. End of the excercise, we change partners, proceed. Later she complains to sensei and mentions the incident to a few others. Sensei says he knows it's not my intention but speaks to me about it. But by that time I had heard it from others, so I sought her out and profoundly apologized to her before sensei found us in that conversation. Equally: no harm done. Yes, she initially thought I was grabbing her boob (hence the startled look), but accepts that it wasn't my intention.
Especially that longer example had the potential to become "a thing" (this was also about two years after that traumatic earlier situation, so I was a lot more sensitive to this). But it wasn't. I've heard that in other martial sports, the focus is more on the "martial" aspect (in our karate, kumite is just one third of the general lesson, with the majority of focus on the "arts" part), and that this draws an audience that's more into fighting. But this is hearsay, as I'm not boxing or doing other kinds of sports...it's hard enough to get a black belt in ONE sports.