These are all examples of the patriarchy in action — and no, I’ve never had those things happen to me, they wouldn’t have done because I’m a male. By the same token you are unlikely to have people assume that you cannot look after children, that you’re emotionally unavailable/immature, that you cannot ask for help or that you will pay/provide things. This happens to men all the time — and they flow from the same oppressive source.
Whilst I may not know your experiences, conversely you don’t know mine — I would argue that being a man and being a woman are different, but both are hard. (If it were a walk in the park being a male the suicide rate for young men wouldn’t be three times as high as any other group in society). The patriarchy has developed and isn’t particularly positive.
However
You cannot opt out of a given system using subjective feelings as the basis for overturning the system in question. You will create an anarchic free-for-all that makes the social order less regulated and far more dangerous for everyone involved.
What seems like social progressiveness in recent years is having the opposite effect to the one intended. The debate becomes less reasonable and division becomes more pronounced. This is where we’re at now, and the world is no safer for your daughter than it was 5 years ago — I’d argue it was more dangerous given the resurgence of anti-female sentiment backlash.
Continuing down the same vein of division for the sake of division will teach each sex to be fearful of the implicit power of the other — arguably that’s a rebalancing of the patriarchy and I can see why it might appeal. However, if we carry on down this route we will replace the male-patriarchy with a female-patriarchy or the two will do battle indefinitely.
The patriarchy affects everyone in different and problematic ways — the only viable solution is open honest discourse of difficult issues starting much younger than it currently does. I think we’d be better off giving children the chance and space to talk to each other as human equals without the adult agenda around to influence and inform them. I’m convinced that the centre ground will ultimately win out and that the happiest people will strive towards a better and more equal set of norms.