From a practical perspective, giving up the newborn for adoption is significantly easier than the 4 month embryo - it's already been carried to term and birthed. And quite a few humans, correctly or otherwise, feel a lot more 'ick' around the idea of infanticide vs. abortion. But they also feel a lot more 'ick' around late gestation abortion too - most states have had gestational limits around abortion. Very few have had none. (Many of those with gestational limits do have exceptions around health/safety issues for the mother, or significant medical issues with the fetus, etc.)
It's kind of a strange argument because most of the US did accept the premise that at a certain point in the embryo's development abortion becomes less acceptable. I can't speak as definitively for the rest of the world, but a cursory google shows that the situation is quite similar - most countries that allow for abortion have gestational restrictions.
IIRC US is quite permissive in that regard? 12-14 is generally standard across much of Europe while in US that’s generally viewed as quite restrictive?
Either of them isn’t a real person, neither is fully conscious. Sure a newborn can feel pain but infanticide can be done in a humane way. What we are depriving from the newborn is the opportunity to live and experience the rest of its life but the same applies in both cases.
And in a quite a few ancient societies infanticide was fully acceptable (killing slightly older children was generally not) and used as a somewhat safer alternative to abortion.