Although I think that women have oracular intuitions more frequently than men (in the middle ages this was attributed to their having more "porous" souls, that is, souls more open to external influence), I think a big chunk of the claims women make are attributable to selective memory and general irrationality.
When a phone rings, a woman might have any number of thoughts or feelings, including a vague dread.
It turns out her relative has died. The dread is singled out and amplified, given a concrete significance, while the many other thoughts and feelings are forgotten. Later, in telling the story, the woman says (and believes) that she "knew" precisely what the call was about before she picked it up.
I am wary of these claims, because I've witnessed this process play out transparently. I think most people making these claims should mistrust their memories, rather than relate them as gospel.
I'm not talking about where a woman takes one glance at a friend and knows there's something up. That happens constantly. Women are without a doubt more attuned to peoples' emotional states, especially people they know, and so long as there is direct sense knowledge (and not just a phone ring or a fleeting thought), the information gleaned from which is not claimed to be strict and precise but only vague and general, I have no particular reason to doubt it.
Speaking of emotional tuning, Frances, I met a young woman this summer who seemed specially attuned to me. She would mirror my emotional states, only boosting the volume several notches, so to speak, slightly dramatizing my typically muted emotions. (Sorry for the mixed metaphor.) A few times it seemed like she was a personification of my internal forum. On top of liking her for herself, I learned a fair bit about myself just by being around her. I guess that's a wordy way of saying she was very sympathetic.
The point is, if women occasionally claiming they have psychic intuitions is part of the collateral for their ability to be so warm and sympathetic, I can live with it.