When studying American history, one must understand that for centuries only white males held certain rights, such as citizenship, voting, and property rights. Although the first colony of Virginia was founded in 1607, women, African-Americans, Native Americans, and other minority groups did not gain many of these same rights until after the Civil War in the late 1800's; by 1900, women and minority groups were still not considered nor treated as equals in many areas of America. Therefore, it is understandable and abundantly clear why women joined in and greatly influenced the abolitionist movement for hundreds of years before the formal Women's Rights Movement of the early 1900's: women fought for all people to be treated with dignity and respect. The organization of abolitionist groups, such as the American Antislavery Society, helped to pave the way for feminist movements, such as the National Women's Rights Convention.
As slavery had been abolished in Europe by the early 1800's, more and more attention and pressure arose to end the practice of slavery in America as well. Women such as Harriet Tubman, an ex-slave and strong abolitionist, advocated that all men and women, regardless of race or gender, should receive protection for the natural rights which John Locke espoused of life, liberty, and property. Other abolitionists, such as Lucretia Mott, Elizabeth Cady Stanton, and the Grimke sisters proclaimed the same message, calling for an end to unfair bias against any American who was not simply white and male. Martha Wright, Mary Livermore, and Julia Ward Howe, who were strong abolitionists, also helped many African American females fight for their specific rights as women, as well.
These women understood that a declaration of equality for African Americans also applied to people of both genders, as well as all races and ethnicities in America. The fight for recognition, fair treatment, equal opportunities, dignity, and respect for one group of people must be applied to all. Truly, this understanding is the basis for the totality of the word freedom. Women fought for the Preamble of the Declaration of Independence to be applied and relevant to all citizens: "We hold these truths to be self-evident, that all men are created equal, that they are endowed, by their Creator, with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness."
Women were avid supporters of the abolitionist movement and they also partitioned the Southerners to end the practice of slave ownership. Lucretia Mott, one of the earliest fighters for women's rights, and William Garrison founded the American Anti-Slavery Society in 1833. It was intended to end slavery and all forms of discrimination against women. Women also supported the emancipation of slaves; in 1863, during the first ever Women's National League Convention, the attendants, mostly women, led by Susan B. Anthony and Elizabeth Cady Stanton, signed a petition to end slavery—there were 400,000 signatures in total. Following the passing of the Thirteenth Amendment, the women saw that it was possible to also gain their freedom. In 1866, the National Women's Rights Convention joined forces with the American Antislavery Society and established the American Equal Rights Association with Elizabeth Cady Stanton at the forefront of this partnership. This organization later dissolved after the passing of the Fifteenth Amendment, which failed to mention women as equals to men. After that, Stanton and Anthony formed a new national organization that focused solely on women. It was called the National Woman Suffrage Association (NWSA). Hence the feminist movement began to gain ground.
https://courses.lumenlearning.com/suny-ushistory1ay/chapter/reconstruction-and-women-2/
https://www.nps.gov/wori/learn/historyculture/antislavery-connection.htm
Douglass was absolutely correct in his prediction, which is not surprising given that he was an early advocate of equality for women, attending, for example, the Seneca Falls Convention in 1848. The abolitionist movement provided a forum for women's political participation at a time when they were denied such a forum by law. Legally, women could not vote, and culturally, a "separate spheres" culture dictated that a woman's proper place was managing the household. But women could form clubs and other organizations that advocated against such societal ills as slavery, Indian removal, and alcohol abuse. Another reason that women played a major role in the abolitionist movement was that it revealed the inequalities that women faced. Women abolitionists found themselves closed out of antislavery meetings and organizations, and this angered them to the point that they began to openly advocate for their own rights, as Elizabeth Cady Stanton did at Seneca Falls. Many of the leaders we associate with the abolition movement were women, including Lucretia Mott, the Grimké sisters, Sojourner Truth, and Harriet Beecher Stowe. As for the debate between the Grimkés and Catherine Beecher, the latter argued that abolitionist demands for immediate abolition were inflaming the South and actually making it more likely that slavery would continue. She looked at the issue as a political matter, whereas the Grimke sisters saw it as a fundamentally moral question. They thought, like William Lloyd Garrison, that the republic could not persist in allowing slavery, which was a mortal sin. She believed in gradual emancipation, an approach that had once been shared by many, North and South, but became less viable as the sectional conflict over slavery worsened after 1837, when Beecher's letter criticizing immediate abolition was published. But overall, the prominent role played by women in the abolition movement remains one of its most remarkable aspects.
http://www.teachushistory.org/second-great-awakening-age-reform/resources/catharine-beecher-opposes-abolitionism