In a world where women had few economic opportunities, where men in the marriage controlled most of the economic resources and where custody was often granted -- especially before the mid-19th century -- exclusively to the father, liberalizing divorce laws was an essential plank in the women's rights platform.
The illustration below, a full page in the original in Life (Volume XLVIII No. 1255 November 15, 1905), shows the situation in which many women found themselves -- tied to a marriage that gave them few rights and few options within the marriage, and many obstacles to ending the marriage.
Shackled to her husband, she reaches towards the gate titled "Divorce" -- but is blocked by a figure who represents both the law (note the police hat and billy club) and the church (note the vestments).
Today, while many claim that women have "all the rights" in divorce, divorced women are more likely to be less well off economically after divorce, and divorced men more likely to be better off economically. Women do not automatically lose custody of their children -- in most cases, the assumption is now that women are more natural or better parents unless there's strong evidence otherwise. And while women's work still does not pay 100% what men's work pays, women have far more economic options.
While it's arguable that divorce today is often too easy, it's also important to remember how much change there has been and why liberalization of divorce has helped to free women from entrapment in bad marriages.