Bossy isn’t actually rude though.
It may actually be a way of sugar coating really quite problematic behaviour. She’s bossy with her peers may be a nicer way of putting she’s overbearing, dictatorial and controlling with the other children. Which some children are. Not just girls.
That kind of behaviour is not good regardless of the child’s sex.
I do think that this kind of dictatorial and controlling behaviour can persist in some girls far longer than it should because sometimes the adults around them insist of framing it as confidence and assertiveness.
I know a 9 year old girl who is surrounded by adults who insist it’s wonderful that she’s so confident and assertive. But she is not. She orders her peers and siblings around constantly. She directs everything and then sulks if anyone deviates from what she wants. She tries to get the other children into trouble if they don’t do what she wants. She tells the other children that they just aren’t as good as she is or refuses to let them try things. Even with adults, she’s domineering and controlling. It’s not adorable confidence when a child is instructing you and lecturing you about your shortcomings; it’s horrible behaviour.
Her mother, I think, is very similar (and her father too in some ways - quieter ways, but he’s arrogant and hypercritical). Her mother struggled at secondary school and had no friends at all - I’d imagine because, actually, the other kids decided that they similar weren’t willing to be ‘bossed around’ by her any longer. She has never learned to be assertive. She’s either in control, manipulating things to get her own way or she’s outright aggressive.
Yes, boys and men can demonstrate similar or worse behaviours. And no one should be sugar coating that either. ‘He’s a bit boisterous’ as a euphemism for ‘he’s aggressive with the other children’ is particularly insidious. And parents are equally (possibly more) likely to run with that euphemism and not address the behaviour.