Personhood

[Shell B]

If a baby is brain dead, would it be logical to take the baby off life support?

Well, to call it logic, you would have to lay out the logic that leads you to that conclusion, so I couldn't really say whether your argument is logical. Personally, I wouldn't do it if there was no shred of hope. It's delaying the inevitable and I don't have the resources. Someone who did have the resources and still managed to cling to hope? Well, it would be logical for them.

I think it's up to the mother, but she will invest a lot on a baby that doesn't even notice, care, want, etc. It's sad. It's the kind of selfish that mostly hurts the person being selfish.

Whether it is selfish or not depends on the person's motive for keeping the baby alive. Say she believes in miracles? Sure, we know it's bullshit, but it's not really selfish if she truly and honestly believes a miracle could happen. Sane? Perhaps not, but it's not black and white.