All those differences do impact roles in society. They let women breastfeed. They give men greater physical strength. Other biological differences make women become pregnant. These will affect roles in society.
I am a proponent of paternity leave. The counter argument is always based on biological differences. So are the arguments for not having women in many roles in the armed forces.
> gender is a human invention.
That is a tautology. It is by definition.
Where exactly is the physical strength of males necessary in modern society?
The only circumstance in which there are men strong enough to so something that women can't do is at the most elite level of athletics. Any role relevant to society that would require that level of strength, we have machines for, because the majority of men and women are not elite powerlifters, and because they probably need way more strength than is safe even for those elite athletes to require all the time.
And then yes women can give birth and breastfeed (though it doesn't seem like being raised on formula alone is much of a problem these days). I don't see why those biological features need to affect roles as much as (some) people seem to think they should.
People with different skin colours have different resiliences to sun exposure, but just because the sun is a big part of our life doesn't mean we NEED to shape society around those biological differences.