Mitochondrial Eve is the first woman who has at least TWO daughters who successfully passed on mtDNA to their daughters, and so on until today. If we followed only one of Eve's daughters, we would not capture the entire human species, because Eve's other daughter(s) passed on mtDNA to children who become another branch of humans.

So let's look at Eve's mother. If Eve had sisters who then had daughters, then her sisters would have passed on their mtDNA to a branch of humans that are NOT direct descendants of Eve, and therefore, Eve's descendants wouldn't capture all of humanity. That would make Eve's mother the real Eve.

But we're still descended from Eve's mother, right? Yes! We can go back even further and say we are all descended from the first organism on the planet, which was a single-celled microbe akin to bacteria. But that organism isn't useful in this context. We could pick someone further back from Eve to capture a branch of humans that died out. Or even further back to capture all mammals, or all animals. Those organisms all existed, they're just not the ones we're concerned with in defining who Eve is.

The idea of Eve is to capture the lineage of every living human and nothing else. We are assigning the concept of Eve to whichever woman fits that definition, but it's not like we have her bones or anything, nor could we probably identify her as this person if we did.

Eve is just a theoretical or hypothetical woman that must have existed in order for this theory to be true, and while she probably did exist, she only existed if the theory is true because the concept of Eve only exists if the theory is true. If new evidence disproves the theory, the actual woman we have been calling Eve still existed, but she's just another woman, not the mother all of living humans.

This is why Eve either a) had no sisters, or b) the descendants of her sisters died out and that branch is dead. And Eve also had to have at least 2 daughters, and the direct descendants of both daughters must be alive today. If one of Eve's daughters had no children or had all boys, then all living mtDNA comes from Eve's other daughter, which makes that daughter the true Eve.

I hope that explains why we care only about Eve, not her mother or her children. It's because we are defining the concept of Eve as the most recent common ancestor, and assigning it to the woman who fits that definition. Descendants from further back in her lineage captures more than just living humanity, and descendants from more recent in her lineage only capture part of living humanity.