Just don't dismiss it. I work with children and their parents and other professionals and I cringe at some of the messages passed on to children by their parents and other education professionals.
"Boys what are you doing letting those girls carry the heavy books? You should be ashamed of yourselves" (from a female TA)
"Oi, Matthew, you're running like a girl. Come on!" (male teacher)
"If he hits you again, hit him back. That's the way a man deals with it. None of this running to the teacher" (from a mum)
"Son, I've told you, boys don't kiss" (dad to a 5yo boy when he picked him up from school at the end of the day and his son went to kiss him)
It's not an 'interesting way of looking at it', it's what happens. These are the messages children are getting every day. We can't then be surprised that they respond to it.
One more thing. When a woman says something to you and you find yourself responding negatively to it, think about how you'd respond to it differently if it were a man saying it. There will be a difference because, until we each address it, we all do it. That's how internalised it is. You don't need to reveal it, but be honest with yourself.
There's also no shame in reading and educating yourself. We are all born into and brought up in this. Until you challenge it for yourself, it will seem ridiculous and unfair and unnecessary. It did to me too, and I'm a woman.