Cats, chimeras and DNA

In Free Culture, Lawrence Lessig argues that what makes us human is our DNA. Writing about chimeras – people and other organisms with two sets of DNA because two embryos fused during development – he writes, “the very idea of DNA is that it is the code of an individual. Yet in fact, not only can two individuals have the same set of DNA (identical twins), but one person can have two different sets of DNA (a chimera). Our understanding of a ‘person’ should reflect this reality”. It is important to note that Lessig’s claim that our understanding of “person” should take into account the possibility that they do not have a single unique sequence of DNA rests on an assumption that DNA is what defines the human as such. His claim for DNA as the code of the individual is widely accepted, but DNA is also the code for individual animals, just the same as it is for humans. Consider for a moment that that DNA of an individual housecat differs from other housecats. Each household pet could be identified forensically by their DNA, just as we do in for humans in crime scenes. To find a cat that is a chimera, with two sets of DNA, would not lead us to question whether that cat is indeed a cat.

But according to Lessig, the human chimera should be taken into consideration when defining the human as an individual with a unique and single DNA signature. How is it that the category of person is challenged by the chimera, while the category of cat is not?

I guess I'm not necessarily expecting an answer - it's just a question that emerged from the reading.