Is Harriet Harman a sexist..? Well as Equalities Minister you'd really hope not, but this pronouncement, as reported in the Telegraph (which to be fair is hardly one of her supporters) casts considerable doubt on this hope:
Here she says that, "Men cannot be left to run things on their own." The point she is trying to make is that there should be a mix of the sexes in the leadership (specifically the Labour Party leadership), which seems reasonable. However if you swap the wording of her statement we get: "Women cannot be left to run things on their own."
Now if any man said this I think it would be fair to accuse him of sexism, therefore the equivalent statement by a woman must be equally sexist. In other words this pronouncement of Harman's is sexist.