The use of all or nothing statements like those you mentioned, on a constant basis, is a sign of mental illness. Now, we all use statements like this from time to time, but the constant use of them signifies a black or white kind of thought process, with no shades of grey.
Combine a mental illness with no father figure, and you have a recipe for diasaster.
Consider that the courts are often willing to listen to those so afflicted while deciding against the father in custody battles, the courts doom children to this sort of exposure, and often with the blessings and assistance of Social Service Agencies who know they will have an enduring caseload as a result.
I won't say the fathers don't willingly leave such a union if it was ever formalized, just that they have little chance of taking their children with them, even if their situation makes that economically possible.
It has been my experience that many of those who constantly use all or nothing statements are afflicted with some form of substance abuse as well, making a sustained relationship with the mother exceedingly difficult or impossible. However, liberals as well tend to use such all or nothing statements in normal discourse, and those in the Social Services industry tend to sympathize, especially with those who know just what the Social Workers want to hear.
At the base of all of that is a cultural morality which trivializes the very relationships, momentary or 'permanent', which lead to offspring. A longer courtship may have precluded the liaison. When we address the moral issues which underlie situations like the one that child is in, perhaps there will be fewer children in those situations.
The 'anything goes/if it feels good, do it' moral standard has been immensely destructive in ways we won't understand until those who study such things can be completely honest about the results.