By "Injustice" Martin Luther King, Jr. means that if a person was being treated unjustly in one part of the world then it was a threat to the laws and justice system in every part. Everyone should be treated equal and fair.
The actual quote of Martin Luther King is-
"Injustice anywhere is a threat to justice everywhere"
The south is subject to the king's blatantly discriminatory laws. He makes the case that there is unfairness, which is a barrier.
What convincing arguments does Martin Luther King offer?
The monarch writes in a letter from a prison in Birmingham that injustice exists everywhere and poses a threat to justice everywhere, and he claims that this is because there are impediments standing in the way of establishing equality and justice. As he claims that the segregation and separationist legislation supported by white people lead to injustice.
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