Is it normal to have a girl/women to propose, be expressive and take upper hand in relation?

Is there anything psychologically wrong in it? Its normally found that man tries hard for his women and women is less expressive; even though she feels much more than him, she acts to be repulsive or in neutral? Is it normal for a women/girl to propose and be more expressive of her needs and take a upper hand in privacy in their relation or pre-relation when she is trying hard for her crazy guy? Is it normal or carry any psychological abnormality? And if it happen when they both are dating for the first time in life?