I do not believe that Hillary lost because of sexism, and I'm a Obama supporter anyway. But was their sexism against Hillary? Without a doubt.
Hitchens, like usual, makes some good points. Unlike the racial divide, there are some fundamental biological differences between male and female. Some of these make one gender better at some things than another--there's an obvious reason men and women's sports teams are separate, whereas a similar division along racial lines would be ridiculous.
Yet this is where Hitchens trips. There are no gender specific characteristics that make a female less (or more) fit for holding a position of power. And certainly her physical characteristics (cackle, cleavage, etc.) have nothing to do with her ability. The fact that the press saw it relevant to comment on Clinton's physical attributes disproportionately to those of Obama is the sad proof that today a woman's overall value/competency is still often based on her appearance. Whether it be job interviews or a political campaign, women attempting to gain jobs in fields where looks ought to matter little are often reduced to the body in a way men do not have to deal with. Is this why Hillary lost? Maybe in part, but as Hitchens points out, there was a lot wrong with her campaign that had nothing to do with sexism. But even if it was not the cause of her loss, it was undeniably there.