I am afraid that I don't have time at the moment to post separately on this, or carry forward the discussion now, but I want to post this as a marker that at some point in the future we could have a good discussion on "rights." Hiram's post reminds me that the issue of vegetarianism is closely related to the debate about "Animal Rights." Due to PD32 and the other Epicurean doctrines on justice, I suspect Epicurus would argue that "Animal Rights" do not "exist" except to the extent we choose to adopt and enforce them.
And I bet you know what's coming next: The same reasoning would lead one to question the common interpretation not only of "animal rights" but also "human rights" and any other kind of "rights" apart from the choice of those involved to adopt them. I have frequently heard it argued in the law that "civil right" is a valid concept, but only to the extent that a "civil right" is something that is validated / vindicated by a civil government. On a desert island, this argument goes, there are no such things as "civil rights" or any other kind of "rights." Of course the issues that we place under the head of "human rights" are among the most important to us of all, and demand our most urgent attention and action to defend them. And yet we ought to be clear what it is we are talking about when we talk about them. As commonly used "rights" is a word often used to imply that there is some outside / superior force that defends and protects them from infringement, and in the Epicurean world view there is no such force, at least in our personal cases as individuals.
I don't recall that anything in Epicurean philosophy supports the existence of any theory of that kind of "rights" whatsoever - even the commonly used term "natural rights." Given the Epicurean view of the nature of the universe, there is no vindicating force that "comes to the rescue" of "rights" of any kind when they are threatened. It is only the action of living beings in defense of their own interests that is ever active to defend any construction of "rights" of any kind.
I know this is a huge subject and demands its own thread at some point - butHiram Crespo's introduction of the topic through "Animal Rights" would be a great place to start. I suspect the two topics are closely related and the analysis of both would be pretty much the same.