Saying "all men" makes it sexist. Calling a man a pig would depend on the context.
The word pig as an insult is not "used almost exclusively against men". Calling a man a pig does generally refer to his behavior while calling a woman a pig generally refers to her appearance.
Sexism is a two-way street, no doubt there are plenty of times men are subject to sexism. I doubt if a female comet-lander scientist wore a shirt with hot guys on it anyone would have made a fuss.
But one has to consider the circumstances and in the case of shirt-man there's a particular history of discrimination against women in STEM fields and a lot of people thought things like the shirt reflected the problem.
In the case of women in positions of power, the sexism is deeply rooted. Lack of awareness or insensitivity to the specific sexist issues in this case such as commenting on looks/voice/clothing and a number of behavioral things, emotional/hysterical (which by the way was a reason to remove a woman's uterus—a hysterectomy was done to treat hysterical women and you can find this in early 20th century medical texts, no joke) is bad enough. But trying to defend such a blatant example as screeching harpy not being sexist when it is pointed out is odd.