Why did the women’s movement of the 1960s in the United States and Europe focus on birth control and sexual freedom?

Part of the focus on birth control and sexual freedom in the 1960s arose from the increased availability of safe contraception. The birth control pill, an oral contraceptive, was approved by the Federal Drug Administration in the United States in 1960. In 1968, the FDA approved intrauterine contraceptives, another effective barrier to pregnancy. For the first time ever, highly reliable birth control meant that women didn't have to worry that sexual intercourse would lead to an unwanted—not to mention, socially stigmatized—pregnancy.
As the 1960s open, best-selling books, such as Helen Gurley Brown's 1962 Sex and the Single Girl, while hardly a feminist manifesto, advocated to ordinary women that they should enjoy sex in or out of marriage. Feminists went further and saw reproductive and sexual freedom as leveling the playing field with men. For millennia, a double standard had allowed men, but not women, sexual freedom and had condemned women, but not men, for accidental pregnancies. Feminists understood sexual freedom as a way to control their own bodies as men did. Feminists embraced the idea that they should enjoy sex and chose their partners, promoting both as signs of equality and autonomy.
https://www.ourbodiesourselves.org/book-excerpts/health-article/a-brief-history-of-birth-control/