Early suffragists including abolitionists saw a woman's condition not much better than a slave's, since she could not own property, control her own income, or seek custody of her children if divorced.
Kentucky in 1890 was the last state to consider women as "chattel property." Women were owned by their husbands or fathers, but could not even own the clothes they wore, even if they made the clothes themselves with cotton they planted and picked.
Temperance advocates thought that if women could vote, they could pass reform legislation that would protect women and children. Kentucky's Carry Nation was a leader in the movement. One contemporary remarked "It's easier to see a drunk than a principle". (info from the University of Louisville)