Ova should not be called "eggs."
We don't call sperm "seed," even though that's what "sperma" means in Greek. That's because spermatozoa aren't seeds, they're gametes, analogous to pollen, not to acorns. Using the word "egg" to mean ovum is the same error as calling sperm "seed." Eggs and seeds are embryos, not gametes.
An egg, like bird's egg, is analogous not to an ovum but to a fetus. We should think off the fetus as in a soft-shelled, water-filled egg. The amniotic sac is the surface of the egg. A mother's water breaking is her fetus hatching. (Whether it's better to say that an unhatched animal "is in an egg" or "is an egg" is a separate issue.)
It's a point of pride for humans that we're not hatched from eggs, as "lesser" creatures are. Back when we thought of ourselves as specially created apart from animals, the idea that we don't come from eggs made sense. Now that we see that we're evolved animals like all the other animals with which we share the globe, it only makes sense that we come from eggs like all the other animals. We mammals may have the special tricks of incubating the egg internally and letting the fetus feed itself with its placenta, but an egg is an egg (and not an ovum).