I recently came across a question asking that in a hypothetical scenario where a doctor has to decide either to save a woman giving birth or the baby birthed. In most of the comments to the question, most people said they would save the woman instead of the baby. Shouldn't saving the baby be morally right as it will live longer than the woman? Furthermore, some utilitarian ethicists believe that it is not that bad to kill babies because they aren't fully conscious like adults and so they aren't "persons". However, the problem with this logic is that these babies will eventually become "persons". If you think about it, saving the baby leads to greater total lifespan and higher average lifespan. So why do most people - even utilitarian philosophers- believe the adult's life matters more than the baby's?
Respectfully, you clearly don’t have a very good understanding of utilitarian ethics. The primary principle is about having the greatest BALANCE of good over bad. Hence, we have to take into consideration a number of factors not just length of life. The mother has developed a personality, has developed consciousness to a much greater extent and understands death , has hopes and dreams and relationships. Obviously, her death, being a rational and developed being has a greater significance. This is the sort of similar to the type of logic we use when making arguments about the value of human vs animal life to draw a parallel. (Obviously babies are not the same as animals, I’m just trying to illustrate what I’m getting at). Second, we have to consider the consequences for others. The mother has relationships, her friends and family, her partner etc. so her death will negatively impact a greater quantity of people more deeply than the baby. Furthermore, her absence in the babies life would also have consequences (single parenthood) Comparatively, the baby’s absence would not be as devastating and the baby is much more replaceable than the mother. Now as for your ‘potential’ argument ; I understand it to an extent, but potential for life is not the same as actual life. It is not convincing enough to justify prioritising the baby over the mother. Surely by that logic, abortions wouldn’t be moral ? anyways, I hope that helps!