In his moving “Letter from Birmingham City Jail,” Dr. Martin Luther King Jr. writes: “We know through painful experience that freedom is never voluntarily given by the oppressor; it must be demanded by the oppressed.” Was he right? Why or why not? Based on what you have seen of the Civil Rights Movement, the Gay Liberation Movement, the Feminist Movement, and the anti-ERA campaign, what do you think are the three most important elements of a successful social movement and why? How can we apply lessons from the successes and failures of these movements to contemporary problems so that all Americans can enjoy the promise of “Life, Liberty, and the Pursuit of Happiness”?

Yes, King was right. Those who are in positions of privilege and power do not usually give up those benefits willingly, even if doing so ensures more equality among all people. This is, I think, an unfortunate aspect of human nature.
The three key elements of social movements (and elements which are shared by all of these activist movements) are as follows: persistence, a clear agenda, and nonviolent civil disobedience.
Dr. King was particularly dedicated to nonviolence, and he studied Mahatma Gandhi's tactic of using civil disobedience to liberate India from decades of oppressive British colonial rule. Though King had detractors among more militant black leaders, particularly Malcolm X, he was the most successful—without him the Civil Rights Act of 1964 and the Voting Rights Act of 1965, civil rights legislation which we still rely to ensure equality in public accommodations and enfranchisement, would never have been passed. In the United States, a minority group's assertion of rights through violence has never been successful in the long term. One of the reasons why the American government antagonized the Black Panthers, despite their embrace of self-sufficiency, was because the Panthers were very assertive of their Second Amendment rights and frequently carried firearms in public. Such images tend to reassert the dominant class's fears of the underclass, which causes the dominant class to seek more control and authoritarian rule. When white America saw the protests in Birmingham in 1963, they saw how committed King and his followers were to nonviolence and how they bravely withstood aggressive violence. It made the country and its leadership ashamed and more empathetic with the civil rights movement.
It is important to remember, too, that rights movements are ongoing. The civil rights movement is not over nor has the goal for equal rights for women and LGBT people been met. Dr. King knew that civil rights would continually have to be fought for if everyone was to be included in Thomas Jefferson's promise of "life, liberty, and the pursuit of happiness." For this reason, after voting rights were won in the South, he pushed for more bargaining rights for workers. When he was killed in Memphis, Tennessee, on April 4, 1968, he was in town to help organize custodians who were being exploited by their employer. Those workers were more than likely to be black because custodial jobs were often the only jobs that black men could get. King's effort illustrated the intersection of race and class in oppression.
The second-wave feminist movement was an outgrowth of the civil rights movement. Initially, it was mainly a white, middle-class movement. Since the late 1960s, the movement has been controversial for its difficulties with inclusivity; there is a dearth of women of color, low-income women, queer women, and disabled women in visible positions of leadership. Like civil rights protesters, feminists marched, staged sit-ins, and participated in public televised debates. The movement generally did not encourage violence against men.
All of the movements that you mentioned were well-organized, capable of rallying large groups of people to participate in protests, had visible and accessible leadership, and had a clear agenda. Movements that have been violent, that have had scattered leadership, and that have had a less concrete agenda (for example, no obstructions for black people who wish to vote, access to safe abortion, no discrimination based on race, gender, or sexual orientation in the workplace) have not been successful.
Some of the radical groups that thrived in the 1960s did not continue their activism because they resorted to violence. Others lost sight of the agenda and fell prey to internal strife and self-destruction through drug abuse. These were the causes of the Black Panthers' collapse by the 1970s.
Modern movements, such as Occupy Wall Street, started out with great potential but had no cohesive agenda (anger at the financial establishment is not enough) and no clear leadership. Black Lives Matter has been successful in raising awareness about the prevalence of police brutality, but each city operates its own chapter under its own guidelines. Though the founders of the movement are very visible, it has been less effective in directly changing practices within police departments. This is not entirely the movement's fault. As the civil rights movement and feminist movements have proven, for any political change to be successful and sustainable, there must also be significant participation from those within the dominant power group.