A sweeping statement is when you generalize a whole group based on one, or very few, examples. I was not generalizing a whole group. I did not say all women are less authoritative etc. I said most women are less authoritative. It was not a sweeping statement as I acknowledged that there will be considerable exceptions to the rule.
In terms of what you say about there being nothing wrong with supporting equality, I couldn't agree more. I'm happy to put my neck on the line and say I support equality more than most, as politically I'm a Marxist, and that's an extreme version of equality. I agree that if there were a women with a suitable set of abilities, then of course they should be given the job. If I were a chairmen, and I had the choice between a man and a woman, and the woman was more suited, obviously I would choose the woman. I just argue that as a football manager, it is more likely to be the man who is best suited to the job due to his inherent advantages. It will not always be the man of course, but more often than not the man will make a better football manager than the women, for my aforementioned reasons.
On your last point, I agree again actually. I tend to get the impression that young people are less inclined to fulfill the alpha male stereotype than previous generations. In other words, yes, men can be seen nowadays as perhaps less authoritative and having greater 'soft skills'. Nevertheless, men compared to women still command more authority. Similarly, women compared to men still have greater 'soft skills'. But for me, commanding the authority of the dressing room is a necessary prerequisite of success as a manager, and for that reason there will always, or at least in the foreseeable future, be more successful men than successful women as managers of football teams.