Most reasonable people would have no reason to think that women commercial pilots are inherently less capable than men. Some of my best pilot friends are chicks.

There is some lingering suspicion about them that comes from two historically legitimate sources:

Military: Fighter/ground attack pilots have to be EXTREMELY aggressive, Just a fact that men tend to be fit this requirement a little better. There are always exceptions. The Clinton folks forced the military to assign some women to aircraft that they didn't belong in, when they would have been just fine in helos or patrol or transport planes. This resulted in some high-visibility fatalities which led to the exposure of unsat training records...women who had FAILED training were put into operational jobs in high-performance aircraft anyway. In the military integrity is paramount, and many officers are still very bitter that their political leadership sacrificed the standards of the worlds most capable military for their own ends. Unfortunately the women involved (who were pawns in the game) and all women in the military have suffered as a result. EVERYTHING about our military is based on competion, and if you have lower official standards for certain people, those people will be viewed as a lower class. The fault is in the system, not in the people.

Affirmative Action: The problem here is that lots of guys want to be pilots. If you have 1000 guys just out of high school, maybe 500 would like to be pilots, 50 pursue it to some degree, 5 get all their ratings, 2 get hired at an airline. With 1000 girls, fewer are interested in the first place...maybe 100 would like to do it, 10 pursue it, one gets all her ratings...Since the airlines go out of their way to hire women, the one with her ratings has a better chance of getting hired than the five guys. The problem here is that you have a larger talent pool to choose from with the guys 2 out of 500 versus 1 out of 100 for the girls. This doesn't mean that the girl is less capable, just that she had less competion to get hired into that reserved-for-a-female job slot, so she MIGHT be less capable but still have got the job anyway. Now if an airline is bound and determined to get a woman through training to meet a quota, then you might have a real problem. This did happen in the past, but I believe it does not occur any longer at most airlines due to some high-profile crashes.

As a CFI the only differences I noticed with women students were that they were usually better at multi-tasking, especially on the radio, but usually had more difficulty with systems. I think this is cultural...in the tenth grade the girls were reading people magazine while the guys were fixing the carburators on the their cars. GA airplanes are a lot like cars.