Why is this explanation so hard to believe?
Because you're not really supporting it. The ratio of unemployment hasn't changed since before
Johnson and the Great Society programs.
Except that right around the same time period that we actively worked to eliminate numerous civil rights violating laws in the south, we were busily implementing those programs. The Civil Rights Act was signed into law in 1964. So was the Economic Opportunity Act. Education, Medicare, Medicaid, and HUD acts were all signed in 1965. Put in perspective, we were still fighting against unfair civil rights violating laws in the US through the late 60s, with the Civil Rights Act of 1968 covering housing rights.
As one phased out, the other phased in. There was simply not enough time to see what sort of socio-economic changes would have occurred among blacks in the US by simply removing the unfair obstacles placed upon them by existing laws. We nearly immediately replaced those laws with a huge system of welfare designed at least in part to help offset the existing imbalances. I think that was a grave mistake that has been the primary cause of entrenched poverty among blacks for the past 40 years.
If we had just removed the legal obstacles to success for blacks and then let things run their course, I suspect that we would not see the same kind of discrepancies we see today.
As noted, it hasn't changed based on what other administrations have done since. It wasn't affected by Reagan's 1982 welfare cuts. It wasn't affected by welfare reform in the 1990's (in fact it became worse following both periods but I don't posit the two are related). It hasn't changed based on wedlock rates. It hasn't changed based on abortion rates. It hasn't been affected by any number of things.
Um... It's a relative number we're looking at though. Welfare programs don't directly target one skin color or another. They target economic need. The effects are different on different groups within the US only because of differences in economic need within those groups. So changing the welfare criteria a little bit doesn't change the relative effect welfare has on those groups. Or at least, it isn't going to change it much. You also have to realize that these programs don't only exist at the federal level. States each engage in their own programs and use federal funding to cover the parts of their programs which overlap the federal guidelines. It's far too complex to simply look at a couple of federal level changes and say nothing happened, so therefore "welfare" isn't a factor in the outcome.
You haven't given them any reason to.
I've given a pretty clear explanation of why and how welfare programs cause harm to the populations who receive them. Instead of addressing that with something like "Oh no! You're completely wrong because people who grow up in households funded by welfare are no more likely to be on welfare themselves as adults", you just point off in another direction.
Am I wrong to say that welfare tends to trap people? Am I wrong to point out that this affect is amplified in communities where a large percentage of the people are welfare recipients? And am I wrong to point out that African Americans are disproportionately likely to live in those communities? I don't think so. So why is it so unreasonable to point at this as a possible (probable even) explanation for the disproportionately higher unemployment among blacks over that period of time?