My twopenneth worth
What children need is a loving, nurturing environment where there physical and psychological needs are met; where they are encouraged to develop and to take (carefully controlled) risks to achieve their full potential; where they do not see lack of success as failure, only a learning opportunity, and where they are cherished for who they are, faults and all. Role models are an important part of this, because they show a child a whole other world available to them, and embody all these lofty ideals in a real person - they are the application of the theory if you like.
IMO it really doesn't matter whether those role models are male or female. That's tired old crap trotted out by the idea fathers are the last line in discipline; that a male child needs to see a male adult being the breadwinner/playing with his DC in order to internalise the idea that this is what males do. As someone who passionately believes that men and women can do the exact same things with the exception of gestation and lactation, I don't need my DS to see a man contributing to housework in order to raise a male child who sees it as his responsibility to contribute to housework. This is because he will be raised to see it as every person's responsibility - irrespective of gender - to contribute to housework. To my mind, gender is very much secondary to all the other human characteristics and traits such as fairness, decency, personal responsibility, self discipline, hard work, co-operation etc should be very much gender blind. And I, as a mother, am just as capable of fostering those in my DC as any father is. To say different is to say that same-sex families are inferior.
The reason we hold up two-parent families as 'better' is mainly because the more adults who are that heavily invested in a child, the better.
But what if that isn't the case? IMO a happy, stable single-parent family is far, far healthier for a child than a two-parent family where there is an unhappy family dynamic, let alone one in which domestic abuse may feature.
The reason that outcomes for single parent families are worse than those of two-parent families are nowhere near as straightforward as many like to believe. One of the factors is blindingly obvious - the reasons that led to the relationship breakdown in the first place! As an example, abuse features more highly in the history of single parents than it does in the general population (busting the myth that women stay; they actually leave and then get punished for it). Or there may have been gambling issues, an affair that led to one party being largely absent, or someone may have lost their job, etc. These will all affect the child regardless of whether the parents stay together or split. But we examine the effects less in families where the parents stay together and choose to focus on single parents.
Furthermore, once you control for poverty, the differences between single parents and two-parent families are actually negligible. And even in families where there is poverty, if the primary carer (usually mum, as is the case in 90% of LP families) has been well educated, even the negative effects of poverty are cancelled out. But it is, of course, far easier to demonise single parent families than it is to accept that maybe we should be doing more to ensure single parents aren't left in poverty - such as maintenance should be considered a god-given right, not a bonus if you manage to get any (let alone a reasonable amount), or making childcare more accessible and affordable, or trying to do more to ensure children from poorer backgrounds don't fall foul of the postcode lottery when it comes to schools and poverty of aspiration.
The world has changed. We know that children need stability, love, education and money in order to reach their full potential. When we accept that there are many ways to achieve this - well-supported single parents, traditional nuclear families, same-sex-parent families, extended families - and stop trying to apply a one-size-fits-all approach, I think we'll have a far happier society.