Where did it come from?
It started with the Nation and a young Malcolm X (before he split from NOI). They felt that King was an appeaser and didn't go far enough to condemn white supremacy and hatred. NOI was about action and aggression while King spoke of non-violent resistance.
MLK was marching in the Deep South in the 50's and 60's. He knew perfectly well that an aggressive approach would get many of his followers killed or worse. The NOI's stance was much easier to carry out in the highly segregated black neighborhoods of NYC, Chicago etc. They didn't understand the realities of what MLK was dealing with. His solution was the most prudent strategy for the types of people he was dealing with.
On top of that, MLK graduated from HS at 15, from Morehouse at 19 and had his PhD from Boston U by 26. His education was in books and he was raised in a solid middle class family. Malcolm grew up a bit rough after his father was killed and he bounced between his mother and then later his older sister in Boston. He was naturally very intelligent but I think he basically ate whatever the NOI was feeding him when he first got out of prison. He was so happy to be clean and reformed that I think he bought into all of the rhetoric without actually analyzing their stances. It wasn't until he got a little older that he realized the flaws in the Nation and developed a more nuanced perspective on the civil rights struggle.
Fast forward to the 80's and you have a lot of older Gen X rappers and socially conscious-types streaming out of Philly, NYC etc. They were looking back at the previous 20-25 years since the Civil Rights Act was signed and felt that little progress had been made. Considering that was the height of the crack epidemic, it's easy to see why they felt that way. There was this idea that MLK "won" the ideological battle but that blacks ended up in a worse position. That if we had applied Malcolm's principles, things would have turned out better. Taking a more militant stance would not have kept COINTELPRO, CIA etc. from pouring drugs into the 'hood. That was going to happen one way or the other. They felt King was soft...easy to call someone soft when you're standing on a street corner in Brooklyn or Harlem surrounded by 20 dozen other black people. It's a lot different than marching through a sundown town in Mississippi where the sheriff, judge and DA are all klan members and lead the white citizens council. None of that mattered. In their minds King failed them and his approach wasn't radical enough.
None of that is really true because King was thought of as a complete radical in his day. You had white supremacists that actually agreed on many issues with the NOI (mainly the ideas of separation etc). No white supremacist ever agreed with King. King got killed because he started talking about economic anxieties with the workers strike in Memphis. That's when he became "dangerous." Just talking about black issues is one thing........talking about the economic divide and attempting to get poor blacks/whites/others on the same page was more radical than anything we'd seen up to that point. There's nothing particularly radical about separating yourself from others. That was the status quo "as-is."