How did feminism contribute to the countercultural movement?
The whole idea of the counterculture was that it was supposed to reject the values of mainstream American culture. During those days, male dominance was one of the values of mainstream American culture. Feminism, then, contributed to the counterculture by offering a challenge to the male-oriented mainstream.
This was done in a number of ways. Two of them were women's rights/liberation and the "sexual revolution." The issue of women's rights was a legal one. Women were pushing to be accorded equal legal status with men. The sexual revolution was more of a social thing. The idea that women had to be chaste while men could be sexually active was a longstanding double standard. Helped by "The Pill" women started to challenge this idea that they were not supposed to be as sexual as men. In these ways (and in others) feminism helped to challenge the values of mainstream America.
Feminism struck at the heart of traditional western culture by calling into question its most fundamental relationships. They emphasized, and continue to emphasize, that gender roles are social constructions, not necessarily biological facts, and that these social constructions amount to a system of oppression. Feminists argued for full political and social equality for women, and this entailed fundamental change in the jobs that women were expected to do as well as the nature of relationships within the home. The questions they raised about gender also paved the way for entirely new movements, most notably the movement for gay rights. Many of the core issues they brought to the forefront, including reproductive rights, pay equality, and equality of educational opportunities, have become mainstream ideas in western society.