I've always likened the modern montra: "It's not a person, it's a clump of cells" to the old pro-slavery montra: "It's not a person, it's just property."
In abolitionist Pastor Theodore Weld's book The Bible Against Slavery, he said (I believe on page 14) that the complete dehumanization of the slave was what made U.S. slavery way way worse than slavery in the Old Testament (which gave slaves rights and in many ways was closer to what we call voluntary servitude). Once a person or a culture has completely dehumanized someone else, they're tricking themselves into thinking that they have no moral restrictions against doing the worst things to a person.
That's exactly what's happening with abortion.