"'No boys allowed' day teaches girls about science and math"
If you think that's just an isolated thing, it isn't. "Girls only" events where "boys/men are not allowed" are in fact becoming more and more popular by the year, in our modern feminist zeitgeist.
These are obviously sexist to the core, and nobody cares (and even if somebody does, they are just dismissed as misogynists... never mind whether that makes any logical sense or not.) However, let's forget about that for a moment. Let's think about what the message is that they are sending to those girls. This is a very implicit message, and it is given completely inadvertently, but it is quite strongly there. And it's quite detrimental.
One thing that one of the interviewed girls in the video says really digs into the crux of the problem: "I think it's a lot of fun because there is no competition."
That really reveals what these "girls only" events are telling those girls. What the implicit message is.
"You will never be able to compete with the boys. You are weaker and less capable than them. If you ever want to learn science and math, if you ever want to succeed in the STEM fields, you will need special treatment. You are not capable of achieving these things on your own, when there are boys competing against you. They are so much better than you, and thus you have no chance unless we organize these special no-boys-allowed events."
Even further, this implicit message leads to even more detrimental thoughts. It leads to man hatred: "The reason why we can't succeed in the STEM fields is because of men; they somehow stop us from succeeding. It's men's fault. The very reason that we need special girls-only events like this is because of men. Without them, we would be much more capable. Men are stifling our academic career; men are oppressors."
Of course this kind of event is not directly or explicitly giving that message, but it easily leads to that kind of thinking. It easily leads to such thoughts (even if just at a semi-conscious level). It easily leads to prejudice and hatred of men. When the message is "I can't succeed in these fields because of men", and if this message is hammered into one's head, it quite naturally leads to resentment and hatred.
And then you wonder why so many women go to gender studies courses instead of STEM fields, and become angry misandrist feminists. Hatred breeds more hatred, even when there are apparently good intentions behind events like this. (You know what the saying tells about good intentions and paving roads...)