Yes you can. Equal doesn't mean equal rolls. It means equal opportunity, respect, and responsibility. A man and a woman should compliment each others traits, not do all the same stuff. The best leaders are those that walk with the people, not those that stand above them.why is a man supposed to take the lead of a person that is said to be his equal? can you lead someone and really be considered equal to them?
your definition of act like a man and act like a woman are outdated in the sense that this is the age of equality not the age of scarce resources where a woman's job is to sit at home and pop out babies, raise those babies, keep the cave together and a man's job is to get that spear and go kill something to feed them all and her value was in the ability that if it came down to it the species needed her for life to continue while he was disposable because any other man could fill his role.
Times have changed but rolls haven't. It's deeper than spears and caves. It's about your character. As a man and as a leader you are supposed to lead regardless of what any one else feels, or does. It's not about who brings the food home or who washes the dishes. It's about you as the man leading your family to prosperity. You make the decisions, not because you are superior to anyone else, or cause you make more money,but because your decisions are what makes the family prosper. If you take the leadership role and do it well your woman will look to you to lead her in the correct direction.
A dictator cannot be equal with the people, but a leader can.