It's not all just about the relationship, but about the father and mother. Both offer very different aspects of life that help children develop in a way they'd never get from something like a 'visiting' parent, let alone the Big Brothers/Sisters program. Those latter things are of course much better than nothing, but the ideal is an ever present father and mother. For but one example, the most obvious is that a father understands what a 13 year old boy is going through in a way a mother never could, yet that mother will do a far better job with that same boy in his early years than the father ever could.

Statistically children from two parent households just do dramatically better by just about every single measurable metric, with 0 control for the quality of that household/relationship.