What is the main claim Martin Luther King makes in his "Letter from Birmingham City Jail"?

In his "Letter from Birmingham Jail," Martin Luther King's main claim is to promote the urgent need for and biblical soundness of nonviolent protest.

King wrote the letter in response to a letter written by Birmingham clergymen, published in the Birmingham Post Herald, protesting against King's demonstrations in Birmingham. These clergymen, although they expressed opposition to segregation, promoted patiently waiting for justice rather than active protest. They also argued that King's protest, while nonviolent, incited violence in others.

King refutes their argument for waiting for justice by pointing out that no gains in civil rights have ever been made "without determined legal and nonviolent pressure," because "privileged groups" rarely give up their privileges without such pressure. He further asserts that individuals are likely to see the truth of immoral actions and be willing to make changes, but groups, whose members solidify each other's views with pressures, never come to understand what of their actions are immoral: "groups tend to be more immoral than individuals." For this reason, King knows that progress in civil liberties can only be made if the group of racist whites holding onto their privileges are pressured into extending their privileges towards others.

King refutes the clergymen's arguments against nonviolent protestation by explaining exactly what steps are taken in a nonviolent protest and how the steps can be biblically justified. In refuting their statement that nonviolent protest should be censured because, though it strives to be nonviolent, it incites violence in others, King questions their logic:

But is this a logical assertion? Isn't this like condemning a robbed man because his possession of money precipitated the evil act of robbery? ... Isn't this like condemning Jesus because his unique God consciousness and never ceasing devotion to God's will precipitated the evil act of crucifixion?

In saying the above, King is pointing out that the violence does not stem from the innocent people such as the man who is robbed and Jesus; it stems from the evil outside of the innocent people. Therefore, the only way to stop the violence is not by condemning peaceful fights against it but by "protecting the robbed and punishing the robber," meaning protecting those who are treated unjustly and punishing those who instigate unjust, violent treatment.