Attending a Deathday Party
Here's my first thought - the natural state of one's soul is to be whole. A broken soul, a soul split into pieces, is no longer natural, no longer whole. This strikes me as a ... bad thing, and hence why doing something bad, something evil, does such a thing to a person's soul. Killing in unnatural, and does unnatural things to the killer - rips their soul in two. This is not desirable at all.
So I think that an act of love, of creating a child - something so natural - shouldn't be something that splits the soul and creates something unnatural. It just doesn't seem right, it seems the opposite of what nature intended. Does that make sense? A Horcrux is Dark magic - birth doesn't seem the way to bring about something so terrible.
And when it comes to the original post, and the question of Harry passing on Voldemort's Horcrux to his children via his own soul: I thought that Horcrux was destroyed, gone from him forever. Now, I could see a good fic bringing it back, but I can't see it being passed down genetically, so to speak. Unless, of course, there was some other magic invovled. Like, a curse or a potion that was used to enable it to happen. Then I could see something like that working.
Hope that helps!