I think this one needs a bit more context. In recent years, at least here in the US, some right wing figures have raised concerns about the idea that there may be some sort of population collapse, where there are not enough young people to keep society running. Their answer to this has been to try to increase the social pressure on women to have more children, and to have them earlier in life.
The argument posted is basically a response to this, making the point that no individual woman has any obligation to society to birth and raise children. American culture is largely based on self-determination and bodily autonomy, which is consistent with this statement. However, this may not be consistent with all societal norms in other parts of the world. Not owing men babies is basically another iteration of this statement, but instead focused on a woman's relationship with her partner instead of society. Again, in US culture, it's generally understood that a couple's decision to have children or not is a co-equal decision between both partners, but again, different societal norms may treat this differently. Not owing anyone an explanation speaks to the idea that the choice is her own, and that she does not need anyone's approval.
So, fundamentally, the logic isn't really wrong. It's just subjectively prioritizing individual rights over perceived collective responsibility. It's also important to point out that there are economic and societal factors that have been named as reasons why people feel like they're less capable of raising children, which isn't really touched on in this argument.