When I think of a strong woman, I usually take it to mean that she has the ability to be independent, she won't fall apart when I'm not with her and she has some ability to handle and roll with life changes without falling apart. Every guy has dated the girl whose whole world revolves around us, she has no friends, and she slowly tries to take away all your friends so she can have you to herself. She gets mad when you make plans that don't involve her, and she guilts you into spending all your spare time with her because she has nothing else. Also some girls just default to useless anytime there is something she doesn't know or a new challenge, afraid to try something new, thinking she can't do it. There is a somewhere in between being as strong as a man and just being another dependent like a child and that's all that is meant by being strong, just don't be useless. Wanting a strong woman doesn't mean the man is abdicating his role as leader or head of household it just means he knows that for a couple to be strong that they need a life outside each other and that a good leader also has to have a strong team to be successful.