I agree with nkozyra.

Many people use that quote for something which is NOT "a reasonable argument". It's been so often misused that it has acquired a meaning different than what MLK intended it to mean. As a result, it's almost impossible to use in a reasonable argument, or more strongly, those who can make a reasonable argument on the topic know to not use the quote because it will be willfully misinterpreted.

Consider the Black Lives Matter movement as a concrete example.

"Black Lives Matter" doesn't mean that no other lives matter, "it means that Black lives, which are seen as without value within White supremacy, are important to your liberation. Given the disproportionate impact state violence has on Black lives, we understand that when Black people in this country get free, the benefits will be wide reaching and transformative for society as a whole." - https://www.thefeministwire.com/2014/10/blacklivesmatter-2/

One reaction to BLM is to argue that "All Lives Matter" and that it's wrong to single out blacks. Some of those who make that argument repeat that famous MLK quote.

But as many have pointed out, this is a fundamental misunderstanding of the BLM movement. See https://en.wikipedia.org/wiki/All_Lives_Matter#Criticism for some of the criticism - which I think are valid.

That is, the "All Lives Matter" reaction serves mostly to cover up or ignore the actual systemic and structural racism which have affected black people in the US for centuries.

Again, with a concrete example, until it was prohibited in the 1970s, redlining was used to segregate blacks and whites. See https://en.wikipedia.org/wiki/Redlining for details. Blacks had higher interest rates, and were often only able to live in poorer parts of town. Until its was prohibited in 1968, covenenta were often used to exclude blacks from the new postwar suburbs. See https://en.wikipedia.org/wiki/Covenant_(law)#Exclusionary_Co... .

As a result, black families in the US generally did not have the same ability to build wealth through home equity that white families did.

Even though those overt practices are now illegal, there are still black people alive who directly suffered from these racially biased laws.

I am convinced that there is a need for reparations, for institutional actions done to people who are still alive. Just like we gave reparations to the Japanese-Americans interned during WWII.

But many oppose any talk of reparations by using that same MLK quote. Because of course any reparations for black people who faced life-long effects of the then-legal racial discrimination must necessarily concern race.

Thus, that MLK quote seems often used as a way to justify ignoring any of the concrete, real-world problems that blacks face.

This is a willful misreading of that quote, because MLK supported reparations - https://en.wikipedia.org/wiki/Martin_Luther_King_Jr.#Compens... .

Now, certainly some people use that quote naively, without understanding how it's been re-appropriated. But this means those people also don't have a basic understanding of the issues involved, which means they are not using that quote as "part of a reasonable argument."

FWIW, My experiences is also that most people who use that quote do so from cherry picking. They don't agree with most of the rest of MLK's views, like reparations (above) or his view that "There must be a better distribution of wealth, and maybe America must move toward a democratic socialism", or his anti-war "Beyond Vietnam" speech.