As already stated, men and women focus on different things. Hence the male captain might not appreciate the way the female co-pilot solve things. On the contrary, do female captains find it easier to fly with female co-pilots?
Important, correct, and frankly worthy of consideration by both to ensure correct outcomes. Has no bearing whatsoever on skill or aptitude though.
The "average" professional male pilot is better than the "average" professional female pilot, in the same way as the average professional male golfer is better than the average professional female golfer.
No data: what could be judged are aspects such as spatial awareness, nevertheless
spatial awareness is proven to be a non-genetic, cutural difference between sexes.
It's easier for women to get employed as a pilot, hence the employers accept less qualified pilots if they are female.
Always a danger if positive discrimination is legal: irrelevant however to the point of the thread - dealing with women (as opposed to dealing with women of lesses ability, of which there are undoubtedly some, as there are men), but dealing with such an issue is not different from working with any other person of lesser competence. Take countries where this is illegal (UK) to make proper comparisons.
The issue with your three comments was the unfounded preconceptions in the second point, and the fuzzy third point, which is not the case in all airlines and countries.
The point is not that any comment portraying women as diffeerent abilities does not have some grounding in reality, but generalising that they are all of lesser ability, when the standard of judgement is irrelevant or misleading.