Isn’t the church quite clear about when life begins? At first breath iirc? Stillborn kids don’t get baptized?

No, Catholics are possibly the most consistent religion in unanimously agreeing life begins at fertilization. (Which, eggs you eat aren’t fertilized anyway.)

They don’t baptize stillborn “babies” because they don’t believe in baptizing dead people, as it’s just a body at that point, no longer a complete person. Plus they believe since there was no opportunity, there is a way to heaven for them in the afterlife.

Fair enough, then the egg metaphor is fitting.