When you write about abortion, it isn't clear whether you really fail to understand the abortion rights position, or you are simply feigning ignorance as a rhetorical device. If it's the former, I'd like to answer your question on the difference between a fetus and an infant.
Many supporters of abortion rights consider self-ownership to be the most elementary and inviolable right of all: We are all the owners of our own bodies. The difference between a fetus and an infant is that a fetus is a part of a pregnant woman's body whereas an infant is not. Libertarians do not want the very visible hand of government rooting around in women's uteruses, telling them what they can or can't do with any fetuses that happen to reside there. Any rights of a fetus are secondary because its existence is secondary to (and until late in the pregnancy, entirely dependent on) the woman in whose womb it is located.
The fact that abortion is a sad business is moot.
James Taranto responds, by arguing that "self-ownership" is an archaic concept, that human as property has been long discredited, and that no mothers speak of carrying a "fetus."Here are four other arguments. Perhaps there are more--feel free to suggest some in the comments section below.