Rosy71 -
Thinking a bit more about your post, I don't think the way that we evolved was inevitable. Our ancestors might have taken a different pathway, or died out altogether. Any number of things could have happened.
I'm glad that evolution took this pathway, otherwise we wouldn't be here.
Looking backwards we can be certain that we are this way through evolution. But that is different from saying it was always inevitable that humans would evolve in a certain way.
On the question of superiority/inferiority...I guess you are talking about the argument that 'women are not cut out to lead'...?
I think it is true that males had more to gain and less to loose in evolutionary terms in competing for status and leadership (as warrior, despot, chief whatever...) because success could mean attracting many women and having control over the wealth to be able to raise many children (100s), whereas for women it made more evolutionary sense to invest in protecting and nurturing the children you have given birth to (at great risk, and knowing them 100% to be yours) than to go out and seek riches and status.
So yes I think this has led to men (on average) tending to have more of the characteristics (single mindedness, arrogance, glory-seeking, all that alpha male stuff) that tend to get you into leadership positions.
But the key distinction to make is that these characteristics don't necessarily make you a better leader, just more successful in becoming one.