The newborn baby still needs to be taken care of, hence the conflict still exists either with the mother or with someone else.
The help involved is not trivial, but it is radically different. An embryo or fetus can kill a woman despite all claims to the contrary simply by being inside her body and attached to it. It can cause damage to her body without killing her, and it can cause serious illnesses. Even trivial illnesses its presence causes, such as morning sickness, can become non-trivial affairs requiring hospitalization.
When a baby is born, it can't kill, damage, or sicken anyone's body any more, because it is outside the body and, being little, it can be controlled by everyone else. Of course, it may be horribly loud, but you can wear ear plugs and still care for it.
The pregnant woman takes care of the embryo or fetus by sharing oxygen, nutrients, and anti-bodies with it and being burdened with carrying in 24/7 for nine months. No bathroom breaks, no meal breaks, no time off after 8-10 hours' work, and no weekends. There is no form of paid labor in the US where a worker can be treated in this way: it's illegal. But of course, the woman is laboring 24/7 and not receiving any pay.
After a baby is born, people can take turns caring for it. They can have bathroom and lunch breaks. They can sleep without laboring. They can hire a babysitter and take the weekend off. Even if the baby is in a hospital, the nurses and doctors aren't working 24/7 for nine months.
If a man was forced to labor physically in the same way as a pregnant woman, he'd call it slavery and he'd be totally correct.