I can give some examples for you, I'm sure after reading plenty of comments in this thread there will be a lot of people who disagree though.
Men, in particular white straight men, have been in a position of power in this country pretty much for the entire time it's been industrialised. For many years women didn't have jobs in any sort of position of power or responsibility. Consider your grandparents, and this parents, when your grandmother's and their mothers were at school, what options did they have? Were they offered further education, apprenticeships or the like? Did they have the same expectations that they could go out and become successful in a variety of different fields? The fact that women these days have more options is great, but it's only a recent development. While we, as men, have male role models going back hundreds of years in company director or owner positions, there are far fewer for women, the expectation and culture for the careers and development of women is still light years behind that of men. Of cousee, there have been some examples of successes, but far fewer than men.
The excuses about women not having to go to war? Why didn't they? Because men said they couldn't be in the army.
Using an example related to this topic a little better, how often have you had to worry about sexual assault in a night out? Have ever had a concern that a woman might have slipped something in your drink? Have you ever been excited to hear about new date rape drug testing kits you can take in a night out? When you do go for drinks, do you have to walk home with a friend to make sure you feel safe in case you are approached by a gang of drinks, or a rapist? I've never ever had to consider that as a man, and yet all my female friends have had to. That right there is a privilege. If you can't see that one example, then you are deluded.