To be a person has, at least in the occidental tradition, been tied to the concept of ownership since Rome. Though it also includes notions of personhood outside of the occidental tradition, we won't be getting into that quite yet. Indeed, to be a person is originally bound to the capacity and desire for ownership, for possessing the property of property. A radical course might be, then, not to abolish animalhood into personhood, but rather to abolish personhood into animalhood. This is why, for Deleuze and Guattari, an anti-capitalist politics requires a becoming-animal. This is just prelude, to summarize the arguments below.
Our word person comes from the Etruscan phersu, which originally meant mask. The Etruscan theater rites held that the performers wore masks, the phersu. These rites would influence the Roman theater, and gave birth to their word persona. The persona could refer to the mask, to the individual wearing the mask, or to the character one played. Persona both meant mask, and also meant role. Around the second Punic War grammarians borrowed the theatrical term of persona, and used is to signify different forms of address (first person, second person, etc.). That was the third century BCE, by the first century BCE the word persona had come to take on several different but related meanings. One had many roles in Roman society; roles as father, roles as citizen, etc.; and persona became the technical term for different types of roles one was to perform in society. Perhaps most definitely for our purposes is that persona comes to be a definitive legal category. One's persona was connected toward the legal right to have a name, that indeed the "Roman citizen had a right to the nomen, the praenomen and the cognomen that his gens assigned to him."  To be a persona meant to have access to one's name, to one's status. And this status is not an abstract category but the very right to have property, to do business, to be a member of the senate. Mauss again:
To the very end the Roman Senate thought of itself as being made up of a determinate number of patres representing the 'persons' (personnes), the 'images' of their ancestors.
It is to the persona that is attributed the property of the simulacra and the imagines. 
Indeed, if we fastforward to 535 CE the exacting Institutes of Justinian codify all of this. As Thomas Collett Sanders explains in his definitive commentary:
Every being capable of having and being subject to rights was called in Roman law persona (see Introd. sec. 37). Thus not only was the individual citizen, when look at as having this capacity, a persona, but also corporations and public bodies. Slaves, on the other had, were not persona. They had no rights (see Introd. sec. 38). [...] Status (legal standing) is the correlative of persona: persona is that which has a status. In Roman law there were recognized three great heads of this legal capacity: libertas, the capacity to have and be subject to the rights of a freeman; civitas, the capacity to have and be subject to the rights of a Roman citizen; and familia, the capacity to have be subject to the rights of a person sui juris. So, at least by the sixth century CE, personhood is the term of art for those with legal standing, and corporations were included. But there is another important development with the concept of person in Rome. We need to rewind back to first century BCE.
While persona was entering legal terminology, it was also entering as a term of art in moral philosophy. In particular, it forms part of the basis of Stoic anthropology. As Cicero declared "dignitas hominis," he also outlined the four persona that make us human in De Officiis. The first persona is that of ratio, of reason. This is the most important one for Cicero, as it is both what divides the human from the animal and "in superiority surpass the brute creatures"  while at the same time gives us the guide of how to treat the other personas, as if they were "wild beasts."  The other three personas are individuality, the historical factors that form you, and your own will. This anthropology is more than just an argument on what separates humans from animals, it is also a moral argument. Here the idea of a moral consciousness enters into our understanding of persona; a moral consciousness that is bound together with reason. Persona will undergo one other important transformation in the classical period, this time under the treatment of the patristics.
As Mauss argues: "Our own notion of the human person is still basically the Christian one." Let's exam what could be meant by this statement. Tertullian, whom invented the notion of the trinity, argued that God is "tres Personae, una Substantia," three roles, one substance. And while we are dealing with three, what we are really dealing with is a duality between spirit and flesh, and this duality must be overcome. This is why Mauss further contends: "It is from the notion of the 'one' that the notion of the 'person' (personne) was created -- I believe that it will long remain so -- for the divine persons, but at the same time for the human person, substance and mode, body and soul, consciousness and act."  The way this dualism is eventually overcome is by tying the notion of persona to the notion of economy. 
These classical understandings of persona, bound up with ownership, reason, legal status, dualism and economy, are important. But we need to fast forward again, this time all the way to the early 19th century.
Antoine Destutt de Tracy, an aristocrat and philosopher perhaps best known for coining the term ideology, published an influential book entitled Traité de la volonté. When Thomas Jefferson translated this book into English, he changed the title to Treatise on Political Economy. Within this treatise, Destutt de Tracy argues for the absolute inability of personal property, because one's very personhood is defined by the capacity to own things. As he writes, "Now this idea of property can only be founded on the idea of personality. For if an individual had not consciousness of his own existence, distinct and separate from every other, he could possess nothing, he could have nothing peculiar to himself." 
Destutt de Tracy's arguments are taken up by Marx and Engels in The German Ideology, which I shall quote at length:
Destutt de Tracy among, and after, many others said the same thing much better approximately thirty years ago, and also later, in the book quoted below. For example:
“Formal proceedings were instituted against property, and arguments were brought forward for and against it, as though it depended on us to decide whether property should or should not exist in the world; but this is based on a complete misunderstanding of our nature” (Traité de la volonté, Paris, 1826, p. 18).
And then M. Destutt de Tracy undertakes to prove that propriété, individualité and personnalité are identical, that the “ego” [moi] also includes “mine” [mien], and he finds as a natural basis for private property that
“nature has endowed man with an inevitable and inalienable property, property in the form of his own individuality” (p. 17). — The individual “clearly sees that this ego is the exclusive owner of the body which it animates, the organs which it sets in motion, all their capacities, all their forces, all the effects they produce, all their passions and actions; for all this ends and begins with this ego, exists only through it, is set in motion through its action; and no other person can make use of these same instruments or be affected in the same way by them” (p. 16). “Property exists, if not precisely, everywhere that a sentient individual exists, at least wherever there is a conative individual” (p. 19).
Having thus made private property and personality identical, Destutt de Tracy with a play on the words propriété and propre, like “Stirner” with his play on the words Mein and Meinung, Eigentum and Eigenheit, arrives at the following conclusion:
“It is, therefore, quite futile to argue about whether it would not be better for each of us to have nothing of our own (de discuter s'il ne vaudrait pas mieux que rien ne fût propre à chacun de nous) ... in any case it is equivalent to asking whether it would not be desirable for us to be quite different from what we are, and even to examining whether it would not be better for us not to exist at all” (p. 22).
“these are extremely popular”, now already traditional objections to communism, and for that very reason “it is not surprising that Stirner” repeats them. 
As Marx and Engels here indicate, there is a stapling together of property, individualism, and personhood. This stapling together is rooted from some of the earliest occidental legal codes and moral philosophy. This forces us to face the idea that maybe we need to exit from basing our rights and ethical responsibilities on the notion of person. It just might be true that as long as the person is the center of our politics and ethics we will always privilege the wealthiest of us and always leave at risk the most disposed. It is for this reason that in some ways corporations are the most natural of persons (who, after all, owns more stuff), and of course it continues to be a problem to ever extend personhood toward other animals.
If I had more time I'd probably now enter into a discussion of Heidegger's notion of animals as poor-in-this-world, Schmitt's notion of nomos, and Deleuze and Guattari's notion of nomos and becoming-animal. But I don't.
A comment on Citations:
I recognize these are not formal citations, it's late and this is a blog. These should, however, allow you get to any of the citations I've given. If you have trouble tracking something down, let me know.
 Marcel Mauss, "A category of the human mind: the notion of person; the notion of self" in The Category of the Person, edited M. Carrithers et al., p. 16.
 Mauss, p. 17.
 Justinian, The Institutes of Justinian, translated with commentary by Thomas Collett Sanders, p. 76. I also suggest reading the strongly Agambenian reading of this code by Steven DeCaroli in "Boundary Stones: Giorgio Agamben and the Field of Sovereignity" in Giorgio Agamben, ed. M. Calarco and S. DeCaroli.
 Cicero, On Duties, Cambridge Press, p. 42.
 Cicero, p. 125.
 Mauss, p. 19.
 Mauss, p. 20.
 Despite his lack of focus on the concept of persona, Agamben's focus on economy in Il Regno e la Gloria is well worth the read.
 Destutt de Tracy, A Treatise of Political Economy, p. 17
 Marx and Engels, The German Ideology, International Publishers, pp. 100-101.