I will assume we are talking about women in America. I think that women ended up fighting for equal rights simply because it was time to do so.
Women are responsible for motivating other women to stand up for their rights. Susan B. Anthony and Elizabeth Cady Stanton founded the National Women's Suffrage Association in 1869. In 1869, Lucy Stone founded the American Women's Suffrage Association. These two groups later merged (consisting of both men and women) and formed the National American Women's Suffrage Association.
Later, during World War 1, President Wilson had announced that the purpose for the war was democracy. Women were outraged and wanted equal rights. It was not long after this that the 19th amendment was passed and women were allowed to vote.