The legal ramifications of a fetus as a person become interesting and convoluted (which is why it is not the situation.)
If a fetus is a person under the law then suppose Fred dies, and in his will leaves his estate to be split evenly between his wife and his children (he has 2 already, by a previous wife). But his wife is also pregnant with twins. But then they are stillborn. Does the wife (as immediate next of kin of the twins) get 3/5 of the estate? Or should she and the two living children get 1/3 each?
Exodus 21:22 deals with a similar legal matter - if two men strife and hit a woman causing her to miscarry, is it murder (life for life?) No, it’s a property crime to cause a fetus to miscarry, pay a fine, because miscarriages or still births happen all the time for assorted reasons, and it cannot be asserted definitely the fighters were the main cause of the miscarriage. Whereas if you hit a living breathing stand-alone human being and they die, it’s usually pretty easy to attribute cause and effect.
The point is - a child born alive and taking a breath is a simple and easy line to draw in the sand. The law hates ambiguous situations where it’s hard to tell if the situation is one or the other, so the fewer such situations, the better.