Why is this seen as an 'outdated' attitude, when the most up to date research confirms it to be true?
It's outdated because it stigmatises women and favours a time when they were chattels.
It's also patronising and completely lacking in compassion. People who split up or are widowed feel shit enough without smug people happily telling them their kids are going to suffer because 'studies' said so.
And actually, I'm not even sure you read these studies widely. Children suffer because they don't have a nurturing caregiver and are living in social deprivation. These factors are CORRELATED with having a single parent, they are not givens.
Plenty of children do perfectly well with one caregiver, provided they have adequate wider support and aren't living in poverty. So a single woman who's solvent and well-supported is just as likely to raise a happy, healthy child as a couple, more so if that couple is impoverished.
Seeing as you care about these children so much, I really hope that you're campaigning for better support for single parents rather than just shaking your head in disappointment at their parlous state and quoting studies at them.