Can I also say, sexism hurts men too. So just because something is damaging to men rather than women doesn't mean sexism doesn't exist.
In fact, this "stiff upper lip" "men shouldn't cry" sexism is far more prevalent in the UK than in most European countries where it's considered manly to be passionate about a subject, so actually sexism is more damaging because it's affecting both genders.
Take, for example, the situation of men, women and raising children whilst working. The very widely held assumption is that women are going to look after the children, taking maternity leave, taking time off when children are sick, prioritise childcare over their careers while men carry on exactly as before. This damages both parents in different ways.
For women it can prevent them getting jobs or promotions at that "fertile stage" (basically if you're between 18 and the menopause you're in trouble), they get mummytracked whilst they've had children, sidelined and kept off important projects because they're considered less reliable.
For men, it becomes a massive taboo to expect a long paternity leave meaning many men don't take it even when they want to, they are expected to focus on work and not change how they respond despite a massive change in lifestyle and priorities, placing an emphasis on spending time with your child, bonding etc is seen as unmanly and so must be discouraged at least within a work setting, when you want a decent work-life balance you're passed over for promotion for a man who "has his priorities sorted" because he doesn't actually take responsibility for his children.
And that is how sexism hurts everyone.