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but it’s not like any sudden development occurs at the moment of birth.
You mean other than breathing its own air and no longer being physically connected to its mother’s womb? I’d call that pretty significant. I would argue that the moment it breaths its first breath on its own rather than as a part of its mother’s uterus, it becomes a murder victim, not an abortion.
Okay, to put it another way:
Once the child is born, it stops being literally a part of its mother and instead becomes an individual.