A Rant on Sexism

I lost my shit today at the park, and very nearly yelled at a little boy who was maybe eight at the most. Girl and I were swinging on the swings. Boy was sitting at the edge of the park watching traffic (his favorite thing to do). Girl got off her swing and walked a few feet away to the merry-go-round (her favorite thing to do at the park). Three little boys were already on it and one of the boys yelled out, "Hey! You can't come on this. No Girls allowed!" Girls face crumpled and tears started flowing down her face.
Normally, I tend to leave kids alone to their own arguments. But boy, howdy! I wasn't going to leave this one alone. I jumped off my swing and got to the merry-go-round in three steps.
"Listen, you little brat!" I wasn't screaming, but it was taking all I had to prevent it. I grabbed the merry-go-round and stopped the spinning, "You don't have the right to tell anyone they can't ride something!!"
Girl got on and I spun all of them until she was dizzy and wanted to get off.
As we walked away, I held her hand. With lips tight and eyes a little teary (but hidden behind my sunglasses), I told her, "Never, never let anyone tell you you can't do something because you are a girl. You fully have my permission to tell them to shut up, and then do what they just told you not to do. Girls are every bit as good as boys. Don't ever, ever forget it!"
Girl looked up at me and said, "I won't forget, Mommy. Next time those boys don't let me on, I'll say shut up."
I don't know, maybe I was being a little drastic, but I look around my town all the time and see blatant sexism that should have gone out of style decades ago, and think about the crap I had to grow up with and get so fucking mad. This might have been a tiny thing, but it's the tiny stuff that chips away at our daughters self image until they lose their shit at 12 and start kowtowing to boys and social pressure and crap like that.
And here I am watching the start of it with my four-and-a-half year-old. So it comes down to am I going to let it pass and let those little punks get away with it because they aren't my kids, or am I going to be angry at the park and have my daughter see me stand up for her and teach her that that stuff is bull-shit and she doesn't need to put up with it. I chose the latter, and I hope all moms with little girls do the same. In much the same way that I stand up for little boys whose parents don't let them play with dolls.