That's not a total ban, Daily Mail.
I agree with these exceptions, except I can never figure out why they include incest. If a 20-year-old woman gets pregnant after consensual sex with her father, why should she be allowed to legally kill the baby?
The theory is that in incest, sex was coerced so it is not unlike rape.
https://en.wikipedia.org/wiki/Legality_of_incest#Laws_regarding_incest_between_consenting_adults
https://en.wikipedia.org/wiki/Legality_of_incest_in_the_United_States
Probably due to the severe medical and mental disabilities such a baby would have, but I think it's more geared toward adolescents who are abused by family members.