Why did women want rights?

They wanted to be treated equally. Decisions about their life were being made, and they had no say in those decisions. They wanted to be able to decide whether to go to school, whether to have a career, whether to marry, whether to participate in politics, whether to have children, etc. Under the old law, women were considered the property of their father, and then their husband. If a father refused to send his daughter to school, there was not much she could do about it. And a husband could beat his wife without any penalty, or take her money (if she had inherited some), or forbid her from working, or force her to have more children. Women wanted to be treated with respect and to be free to make choices, rather than have someone else make all the decisions for them.