She's probably speaking from her experiences.
Women who say this usually do so because they had a baby by a man who turned out to be no good and their sentiments regarding these topics are due to frustration of her child's father not being present or doing enough for their son.
It's not so much that she believes a boy doesn't need a father but considering the circumstances she herself and many other women find themselves in, they'd rather do it alone than have some man living in their house not providing, not just financially speaking, but also emotionally for his son as well as the mother of his child.
Sons need fathers but they also need quality fathers.
Any man can be a father, but it doesn't automatically make him a good one, there's plenty of guys with sons who have done little to nothing for them but expect to be peddled as a “father” when they never acted like one from an emotional/sentimental standpoint.
Someone such as myself and my siblings who grew up in a married household could say we're lucky to have been born in a good situation but not every child has that luxury.