One of my friends was asking me this week about the plight of Cynthia Carroll, the boss of Anglo American and one of the only female CEOs in the FTSE. If you haven't seen the story, Cynthia's apparently coming under the cosh from some of her shareholders, who are questioning her record and pushing her towards a merger with rival Xstrata (which would almost certainly see her booted out of a job). 'Isn't it a shame she's getting all this stick?' my friend asked. 'I'm sure there's something dodgy going on.'

I found this conversation a bit strange, for several reasons. For one thing, my friend doesn't really know anything about the ins and outs of what's going on at Anglo American, or anything about Carroll herself. All she knows is that she's a high-flying woman, and high-flying women are still a bit of an endangered species in the City. So she's automatically sympathetic towards her. What's more, she assumes that I'll also be automatically sympathetic towards her - presumably because I'm also a woman, and I'm also trying to make a splash in the shark-infested corporate world.

But to be honest, I'm not sure I am, really (and not just because I find this kind of pigeon-holing a bit annoying). In principle, I admire Cynthia very much, on the grounds that it's clearly not very easy for a woman to get to the top of a big company (judging by how few of us seem to manage it), and it must be harder still in an industry like mining that's always been pretty male-dominated (and a part- South African miner at that). So on paper, it's fair to say she's a great role model for any woman in business who aspires to lead.

On the other hand, I don't know the woman from Adam (well, Eve). I have no idea whether she over-paid on all those deals, because I know nothing about the industry - but let's face it, it's quite possible (she certainly wouldn't have been the only one). And having never met her, I have no way of knowing whether these shareholders are fed up with her because she's not very nice, or even not very good. Of course it could be that they've cooked the whole thing up on the golf course with the boss of Xstrata because they're sick of their boardroom smelling of perfume, but how would I know either way?

The other point is that Cynthia's a 50-odd-year-old American businesswoman who's spent her whole career in the mining industry. I'm not. In fact, as far as I'm aware, we have absolutely nothing in common, apart from the fact that we've both got an extra X chromosome relative to the vast majority of the occupants of Britain's boardrooms. But does that mean I ought to feel some kind of special allegiance to her cause? For all I know, I might personally have more in common with Richard Branson, or Stuart Rose, or Terry Leahy. (Well, maybe not Terry.)

I'm not sure whether this makes me a terrible feminist, or a very principled one. After all, presumably the goal is for women to be treated equally to men (I don't think it's to get favourable treatment, is it? Although personally I wouldn't mind that at all). And given that men presumably wouldn't expect sympathy from men per se, maybe Cynthia doesn't want my sympathy just because we're both women.

Or perhaps she'd be happy with any friend she can get at the moment, whatever their reasons...