I suspect you're right about the first part. That makes me sad, because I'd hope we'd be more even-keeled as a community.
I haven't seen any evidence that the second is true, though. I've not heard of a plausible mechanism by which - all else equal - men would be better at abstract reasoning than women or vice versa.
I haven't seen any evidence that it's false, though, either, and there are obviously physical and mental differences between sexes/races/whatever, so it seems more likely to me that this would follow the rule, rather than be the exception.
I haven't seen any evidence that the second is true, though. I've not heard of a plausible mechanism by which - all else equal - men would be better at abstract reasoning than women or vice versa.