I have to agree with your ex op, the stats do state that children from broken homes don't do as well as children who have always lived with both parents, there are always exceptions.
I don't know why that is, it may be because there is a high prvelance of affairs/lying/cheating/arguments in marriages that split.
If it is the trauma of parents and children going through the grieving process, and the additional difficulties of step families.
If it is the diffuclty of financial difficulties, and bitterness at nrp who will do anything to get out of paying.
It could be to do with a lowered self esteem if nrp is an arse with contact, and goes off and plays Dad with new g/f and her kids, or has kids with new partner and abandon's his first family of kids.
It could be that the resident parent is less likely to be a sahm.
There could be many more reasons, and if you add them all up, it is not going to make for an easy start in life, and it is no wonder children from broken homes don't do as well.
It doesn't mean that children will definatly not do well, they are statistics, and you have to do the best you can to ensure that your children reach their full potential in life.
If you are living with someone you are arguing with continually, who you can't trust him or he is abusing you or the children then get out!