Children really do need a father

In a study of studies reported here Children Who Have An Active Father Figure Have Fewer Psychological And Behavioral Problems it would seem that a research consensus is emerging in favour of having positively active fathers involved in children's lives. "The researchers are urging healthcare professionals to increase fathers' involvement in their children's healthcare and calling on policy makers to ensure that fathers have the chance to play an active role in their upbringing." The difficulty, as so often, will be to encourage this without stigmatising and devaluing the parenting of those who cannot at any particular time, fulfil that ideal.
What I'd like to know, beyond this, is what is it about the involvement of fathers that makes these kinds of differences? And would that relate to using fathering as a key metaphor in relating to and thinking about God in Christ?