By having total autonomy, some women who don't have the courage to raise a child will choose life. Many places have drop-off provisions at places such as fire, police, or hospitals. Occasionally there are reports of situations when authorities try to find the identity of the mother. That's unacceptable, since the reason for the concept is so a mother has no reason to abort or abandon an infant.
Of course it shouldn't be that way. In an ideal world all mothers would have the moral courage to save their infant. But it isn't that way. This provides a mother another option.
More information when you leave off a pet? That's okay. They're "apples and oranges" situations.