The instance of the argument Vocab suggests is nothing of the sort, though at least he admits that it is an argument about another subject. Here's the quote as Vocab presents it:
From the other end of things, a recent New York Times article featured a similar argument (although his piece was on a broader topic than abortion):The quote is from a New York Times editorial by neuroscientist Michael Gazzaniga about the difference between reproductive and therapeutic cloning. Here's the quotation in context; it's the ending of the piece:Look at your loved ones. Do you see a hunk of cells or do you see something else? … We do not see cells, simple or complex – we see people, human life. That thing in a petri dish is something else. 
In his State of the Union speech, President Bush went on to observe that "human life is a gift from our creator — and that gift should never be discarded, devalued or put up for sale." Putting aside the belief in a "creator," the vast majority of the world's population takes a similar stance on valuing human life. What is at issue, rather, is how we are to define "human life." Look around you. Look at your loved ones. Do you see a hunk of cells or do you see something else?
Most humans practice a kind of dualism, seeing a distinction between mind and body. We all automatically confer a higher order to a developed biological entity like a human brain. We do not see cells, simple or complex — we see people, human life. That thing in a petri dish is something else. It doesn't yet have the memories and loves and hopes that accumulate over the years. Until this is understood by our politicians, the gallant efforts of so many biomedical scientists, as good as they are, will remain only stopgap measures.
Vocab has removed a critical piece of what Gazzaniga wrote--he's not making anything like an argument from size, but rather an argument much more like my position, as seen in what Vocab omitted with his ellipsis and immediately following what he quoted. The piece as a whole is taking issue with the conflation of reproductive and therapeutic cloning, with the idea that the latter involves creating cloned people, and Gazzaniga's position seems to be that this confusion occurs because people are thinking of and talking about undifferentiated cells as though they are people--the same thing that is occuring in this very debate. (BTW, the president's Council on Bioethics, of which Gazzaniga was a member, argued that therapeutic, but not reproductive cloning should be permissible. My view is that while there are currently issues of knowledge and technology that could result in harm to cloned people, in the long run I don't see any ethical difference between reproductive cloning and natural reproduction, so long as the products of each get equal treatment on the same standard of personhood.)
Vocab suggests it would have been better to call this the "just a bunch of cells" argument, but that's really not an argument based on size, but rather an argument based on structure, function, and capacity--which is a good argument! I suspect that this is, in fact, the sort of argument that Klusendorf is misconstruing.
Next Vocab gives an argument from essences:
can any living being become anything else besides what it already is? How can something become a person unless its essence is already personhood? If the color blue is only blue and not the color red in the same way at the same time, its very essence – its fundamental property – must be blue and not red. Another example is that of the tadpole and frog. The tadpole is simply a name for a specific stage during a frog’s development. If one were to terminate a certain tadpole, then a certain frog would be terminated and no longer exist. This means you did not come from a fetus you once were a fetus.The answer to the first question is clearly yes--there are all kinds of metamorphoses that occur in living things while they are alive, including changes of shape, color, size, and sex. And when they die, they can become parts of other things--just as other things become part of them when they come into existence, develop, and change. The second question is, I think, flawed. First, I don't think it's correct to regard personhood as a fixed, unchanging property. Douglas Hofstadter's book, I Am A Strange Loop, argues that self concepts not only develop over time, but can be shared across persons. Second, the question implies that anything that is a person is always and eternally a person and cannot be constructed out of something else. But on everybody's views, human beings are biological organisms, which come into and go out of existence in virtue of the states of their underlying components. Both the view Vocab has been defending and mine say that there are biological components which are not persons, which through some change of state subsequently become persons. If Vocab wants to hold a view by which personhood is an essential property of a simple substance, then he can do that by holding a dualistic view of an eternal soul which is a person that attaches at some point to a human as a biological animal. But if that's his view, then that's the argument we should be having, rather than one in which Vocab is defending a view like animalism.
Vocab makes a subsequent statement that I think vividly illustrates the error in his view:
One way to think about the idea of probability (or potentiality) is that every adult was once an unborn person, just as every oak tree was once an acorn. An acorn is simply a mini-oak tree, just as a microscopic person is a mini-human.But that last sentence is just false. Acorns are not miniature oak trees and zygotes are not miniature people. That's precisely the error that Gazzaniga is warning against in his article.
Vocab subsequently makes a point about skulls being crushed in an abortion procedure, and on that point he's correct--embryos do develop into fetuses, they do develop identifiable distinct parts and functions, and at some point they do become miniature people, but they don't pop into existence as such.
Continue to part four.