It starts at birth doesn't it...and also by that I mean the pattern and behaviours that carry forward to the next generation so the male privilege is self reinforcing.
So thinking of the previous examples of men being leaders without being control freaks or bossy - Boys are treated with the same privilege as men, so when they tell other kids what to do it's classed as leadership where girls are told not to be bossy or domineering. Boys begin to think this is how it is and see themselves as in charge and women as less able (which of course being undermined all the time many women will be less able due to the uphill battle they face) and so the patterns continue when those same adults imprint it to their children. Then men continue take for granted they can fulfil leadership roles without even considering their behaviour to be anything but leadership quality. It doesn't help that these qualities are masculinised anyway, that is they are idealised male traits to start with meaning women inherently cannot have them.
Obviously it's not this linear and the issues are complex but the patterns are strong enough to see trends of how men and women are viewed differently play out the same over the world.
Other things I feel men have to deal with less:
Situations where simply being female means you have to explain yourself so that your gender isn't blamed on why you did or didn't do something. Eg - if I can't put a flat pack together then it's not because I didn't have the right tools or just read the instructions wrong, it's because I'm female and simply can't do it. If my husband can't do it it would be because he was distracted or in a rush.
Low expectation for men to look after children obviously and therefore less burden of responsibility for day to day care of children, which usually extends to the rest of a shared life hence so many people struggling with unequal division of domestic labour.
Women work more for less - if taking unpaid cleaning cooking and other domestic jobs into account then it is even more skewed. So men are paid and valued more. The implicit power imbalance here will be unnoticed by many men as it's all they've ever known.
Men aren't treated as idiots by older men of a particular type. The very fact you are a women makes you irresponsible, emotional and unsuitable for many things in the minds of plenty of people in positions of authority and power. Knowing this makes you shrink a little inside sometimes. Men won't feel this.
Respect - I have to work harder to get people to respect me in my workplace simply because I'm a woman. I don't think many men can truly identify with this because it's a build up of years of being belittled and ignored. Men largely will not have to contend with this.
The majority of people are so unaware that they categorise their children, relatives, friends, colleagues according to the very polarised gender stereotypes that it feels to me like the problems are going to get worse before they get better.