I'm afraid I've never heard someone try to argue about the difference between calling it the zygote stage of human life and a human zygote. It's just two ways of labeling the same thing. I don't know that I've ever seen or heard someone deny that the zygote is a stage of human development.
If I'm reading this right, you are trying to compare a zygote to a newborn as though they are the same. Certainly they are the same organism at different stages of growth, but there are massive anatomical/physiological differences in the two stages.
There is a difference between acknowledging that the zygote stage is an early step in human growth and development and acknowledging that a human zygote itself already is a human being. And there in lies the rub.
You might be surprised how many would even disagree with you that a human zygote is even an organism... let alone a human one.
I think there is still a lot of semantics here.
To keep things light, I'll use a flippant example. If you ask someone, "Which came first, the chicken or the egg?" you will rarely hear people complain that the question is invalid because an egg IS a chicken.
I've seen people describe early developmental stages as not a human being. I prefer not a person. A zygote does not have a brain, nor any other organs, for that matter. It isn't even the "clump of cells" so often talked about in abortion arguments; that would be more accurate for a blastocyst. A zygote is, so far as I can tell, pretty much just the cell formed from fertilization, once the nucleus of the spermatozoon and ovum merge. I would be fine describing that zygote as a human being but not a person. I think the intent is the same, however: differentiating between a thinking, sentient being and one that is not.
I don't want to argue our positions on the value of a human life at any given stage of development. It tends to be one of the more pointless arguments possible; I don't recall ever seeing someone actually change their position on the subject during a discussion or argument. It might be best to clarify terms if you're going to argue about it, though. As it stands, you seem to be trying to catch people in a semantic trap rather than making a strong point.