The reason religion is so powerful

[John 6IX Breezy]

Neo's reasoning was that the embryo is biologically human from conception. Any undamaged human cell is biologically human. Being biologically human doesn't make something a human being.

Right; he is using human as a noun—the embryo is a human being from conception. You're referring to human as an adjective—human hair.

Here's a word I learned from vulcanlogician: totipotency. It's the power of a cell to produce an entirely new organism.

So human genetics + totipotency + any other relevant factor = New Human (noun) organism.

Human zygotes meet this criteria. But without the cells in your cheeks achieving totipotency, for example, we cannot compare them to zygotes or call them human beings. Once they do that's another story.