To be honest, I'd say the people who go on and on about little girls being weak and wimpy to little boys below the age of 5 are probably the real outliers. I must admit though, I'm curious as to how you managed to miss out on the subliminal messaging about women being mommies and men being daddies as a smol child.
Gender is probably best understood as long as one understands that it's not really possible to understand perfectly. For the most part, gender is an internal, mental/metaphysical part of a person that may or may not be present, much like sexuality or empathy or a sense of humor.
It's primarily about identity, but to say that it's divorced from the physical entirely is also to do it a disservice and bark up the wrong tree. So, too, its existence as a social construct and identifier shouldn't be dismissed and forgotten as irrelevant to grasping the concept.
In a way, it's like the really, really old definition of a mystery, like in the religious sort of paradox-but-not-quite sense.