In the video linked, the man said that this is what happened. He claims he witnessed it first hand growing up in a black neighborhood in the 60s.

I obviously didn't link every source, but you can find much more (including first hand accounts) with a quick google search.

Children raised by single parents are vastly worse of than children raised by 2. Every known statistic points to that. There's a reason monogamy was naturally selected into human biology. Raising children is a 2 person job by nature. The proof is in our DNA. You have no ground to stand on if you want to argue that single parents don't have a much harder time raising their children.

If single parents on average do much worse on average, welfare started the cycle of single parents in the black population, and the rate of single parents in the black population has increased drastically (starting at Great Society), then why can't I come to the conclusion that the way welfare was rolled out in the 1960s caused a great deal of harm to the black community?

You can basically only argue one point. Welfare didn't cause the increase in single parenthood. You have no proof of this. The statistics favor my claim, so you're argument falls flat.