There is a fantastic book called "the book you wish your parents had read (and your children will be glad that you did) by Philippa Perry. There is a section on your child's environment where she discussed the findings of a multitude of studies that reach the same conclusion: the structure of the family matters infinitely less than the people within it. Single parent children do no better nor worse than those from conventional families once factors such as financial situations and parental education are taken into consideration. That is to say, whilst single parents are more likely to be worse off financially, that isn't the case for everyone. Definitively stating that this child will be worse off for their mother's single status is disingenuous. Numerous studies also suggest that as long as a child has positive male role models, the absence of a father has little to no effect on the child. The language in which we discuss a father's (or mother's!) absence makes all the difference. For children who's families create an environment of security and nurturing, an absent parent can have no negative effect at all on a child. Of course I may get some replies with anecdotes and this won't be the case for everyone, but bear in mind there are numerous external factors that also contribute to a child's psyche.
I was recently re-watching Grange Hill, in one episode there is great scandal, and an almost-sackable offence, that a single and never married teacher has a child. It's still very much ingrained in us today that being a single parent is a negative thing, where it doesn't have to be any more, nor should it be.
We all impart some level of trauma (however minor it may be) onto our children, no matter how perfect and loving we may be. My parents are still married, they had 2 children including me, upper middle class, job security, grandparents are still married, I suffered no abuse. Absolutely textbook perfect family and perfect childhood. My father was military, and was away a lot though. This was made such a big deal of, the fact he was in danger was talked about so often I developed a lot of complex emotions as a child, that I never worked through until I was an adult. I worried my dad would forget who I was and I worried that he would die. The reassurance I needed wasn't met because the adults in my life were worriers who were also stressed that he would be flown home in a box. It's important to choose your language and tone around your child, being a single parent is only a negative if you allow it to be, as with everything else associated with families. I co-parent, and I reinforce how great DD's dad is to her and how much we love him and he loves her- even when he falls short of the mark at times. His failings are an adult thing to deal with and she isn't an adult, so it isn't discussed anywhere near her. Of course separated parents who constantly criticise and bitch about the other parent, absent or present, are going to raise children with issues around their parentage, and thus issues with who they are themselves.