Of course, for Equality of Chance to be properly implemented you need to do away with as many barriers to it as possible but you should be willing to accept that no matter what you do, there won't be a perfect 50/50.
From all evidence we have, there is strong evidence that male and female humans grow up differently independent of their social surroundings, for example, we found that the brains of newborns can be easily distinguished into female and male as little as 1 month after birth, before any social factors have had much chance to get deep into development.
From that I find it easier to believe that there will be some statistical biases in one direction or another (like how will have, on average, a bit more height) outside of the purely physical domain.
I would rather see some evidence that despite all the physical, hormonal and developmental differences in male and female humans, there is absolutely no statistically significant difference in the brain and/or mind.
More desirable to whom? To the one with the worse outcome equality of outcome will always be more desirable than equality of chance. Plus, from a probabilistic point of view, wouldn't equal chances mean that for large numbers of trials (people) the outcome would also be equal?
> I would rather see some evidence that despite all the physical, hormonal and developmental differences in male and female humans, there is absolutely no statistically significant difference in the brain and/or mind.
You cannot even properly define what you mean by "brain and/or mind", which is why it's impossible to convince you that there actually is injustice if your opinion relies on that. But, for the moment suppose there is some convincing theory which explains naturally why less women are in STEM. Then why would we have to adjust our society to it, as it would benefit from less social tensions if there was equal outcome? Your point has to be much stronger to justify the inequality, as in everything would go downhill super fast if we had equal outcome. Otherwise there will always be social tensions and you have to learn to live with the "feminists".
Yes. For most people those two options would be the same, which is why the difference between those two options matter.
Equality of Chance merely means that everyone gets a shot at becoming, for example, a Math PhD. You still have to put in as much elbow grease as everyone else and work just as hard as everyone else. If female and male humans are equivalent mentally then the end result should be a 50/50 distribution.
If there are mental differences then the distribution would be skewed but it would be fine since everyone has gotten the same chance as everyone else. It's the approach with the highest game-theoretic fairness; the chance of winning the game is directly related to the skill you bring to the table.
>You cannot even properly define what you mean by "brain and/or mind",
With brain I mean just that, I don't know why it lacks definition. I mean the raw organ of thought in the human skull. There are notable differences, as mentioned, found at early stages in the brain that are sufficient for a computer or human to identify the gender or sex of an individual with a higher-than-chance probability.
With mind I was refering to the mental capacity and properties of an individual, ie how good they are at math, their social skills, IQ score, pain tolerance, etc (these are just example categories, not necessarily categories in which a significant difference exists).
>which is why it's impossible to convince you that there actually is injustice if your opinion relies on that
It is certainly possible to convine me of the opposite, I have clearly formulated which evidence would be sufficient.
>Then why would we have to adjust our society to it, as it would benefit from less social tensions if there was equal outcome?
That question feels slightly loaded since it proposes that an equal outcome leads to less tension. Current movements concerned with an inequality of outcome do only so because it is unfairly inequal.
Not a lot of people complain when the outcome of the game is inequal but fair (for example, nobody minds that someone with low strength will be unable to participate in olympic weight lifting, there is an unequal chance of participation and outcome, but it's a fair process)
The resolution to the problem of "do we have to adjust society" is another question "is the reason we are suggesting to change due to a fair or unfair process?".
[footnote]: Fair and unfair are defined as the ability of a player to apply their skills and get an equal amount of reward to other players with the same skill level (or with neglible difference)