I have 2 kids and I have some sympathy for the family and I can say that before having had my kids I wouldn't have.
4 kids here and I have to agree with that... it's kind of appalling that so many people believe a 2 year old is not really a person and has no memories that hold any value, but I suppose I can understand how someone that has had only brief interactions with 2 year olds can think that. A 2 year old is definitely a person with thoughts, feelings, memories, and a personality, and if I lost one of mine at 2 and thought there was even a slim chance at preserving them, I'd do it. I still think it's rather silly to get all attached to fetuses and embryos though.
How much do you remember from before the age of 3 or 4?
Not very much NOW ~26 years later, but ask a 3 or 4 year old how much they remember about their life and they can tell you quite a bit.
I'm guessing the parents' hope is that advancements would happen within their lifetime so that they get to continue raising their daughter from where they left off; not so much that their 2 year old has some kind of knowledge or memories that will make her important to the future.
Most people don't remember events from when they were 2 years old.
When they are still 2 years old, they do.
Mediocrity finds safety in standardization. -- Frederick Crane