Anecdotal evidence does not prove anything. Not having a father does not doom anyone to failure, and it doesn't mean you're going to be a criminal or any of those things. BUT the chances of falling into crime are much, much higher, the chances of succeeding academically are much, much lower etc, etc. Part of this comes down to the fact that in a single parent household, there's a higher chance to be in poverty (doesn't mean you will be impoverished, but one income can easily do that), and the parent has to work a lot more to provide for the child(ren), so therefore has less time to nurture them and teach them.
A lot of our learning happens in our early years. In general (again, not always), it is more difficult for a parent in a single parent home to give the child the attention and time needed because they have to work so hard to provide. Then when they get home they have to do all the housework (when the kids are young), and they just don't have the energy or time to do all they would like to with the children. In addition, young mothers can't stay at home as long after they had a child b/c they need to make ends meet. Lastly, even when they do opt for day-care's, it is difficult for a single parent to afford the "best" ones (which are the ones that give the child a lot of face to face attention and don't have too many kids in comparison to the caregivers, I think it is 3-5 kids to 1), and the child lags behind. When a child is behind in their early years, they are basically playing catchup to all the other children in grammar, vocabulary and all these early learning things and will generally struggle through school. And some of the problem also comes in that these worn out parents who are working so hard think "well I can just put them in front of the TV, but with educational programs". Sadly, it just doesn't work, and it is the face to face talk time, yes, even to infants that builds a child's vocabulary and grammar even before they have started to speak.
The ideal where a child from a single parent home does extremely well does not make single parenthood something to be neglected b/c "well some of them do well". We don't want some, we'd like a situation where the majority can do well, not just "some". Yea, but how are they faring in comparison to other children from more stable homes, or from two parent homes (single parenthood does not equal lack of stability), and the answer is the majority are not faring very well.
This is proven in every way possible, it doesn't matter if one is white, black, hispanic, chinese, indian, whatever the culture, race, background, etc. The reason it now comes down on the black community is that in America, the black community has a disproportionally high amount of single parent, no father homes (and this is not specifically talking about widows/widowers though they definitely need to be considered, but generally kids born out of wedlock).
Anyone who comes from a single parent home shouldn't feel they are inferior or anything like that, but one's goal should be to change that situation in future generations. This is a much more honorable task than to try and defend single parenthood, thinking that those pointing out the difficulties with that situation are attacking them and who they are.