Some people think that to use the Declaration of Independence as a text for political theory is corny, although why one would substitute say Ayn Rand from the Right or Marx or any number of Leftists is beyond me, as to if there is anything radical about Vice Presidential nominee Ryan saying that rights have divine or in some sense non-human origin.
As to be argued below, there is nothing radical in such an argument at all, and those on the Left who wish to smash that argument should think carefully about doing so, as all arguments that rights are contingent lead in extremis to the gas chambers, gulags, nuclear war and such horrors.
Infanticide for example has been justified by Princeton scholar Peter Singer on exactly such human based reasoning, for an example of the dangers of unmooring States from some form of divine sanction, even if one, like Plato, regarded that as a "Noble Lie."
But as to Ryan saying rights have non-human origins, just read the Declaration's opening text.
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn that mankind are more disposed to suffer, while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security."
In the author's view, that remains the most compact statement of modern political theory, noting that where do rights come from in the Declaration of Independence?
Rights are an endowment of Our Creator.
As to why that remains a useful concept, many human lives in a narrow sense are displeasing to some.
For the Left, the lives of the rich are displeasing, which is why radical leftists have always objected to the Lockean definition of freedom in the Declaration.
For the radical Right, the lives of the weak are displeasing, if only for aesthetic reasons as to "deformity." That is why the first people the Nazis came for were the mental patients, since as a practical matter, many of the severely mentally ill are inconvenient to society in narrow utiliatrian terms, if once one admits that principle, the State truly can become a terrifying Leviathan indeed, something the modern Left ought to see as a danger to bashing someone just because they think "rights" as such have non-human sanction.
Now of course, what people often do is stop at the first sentence, and therefore miss the true brilliance of Franklin and Jefferson, as to the relationship between Natural Law of "Self-evident" and "endowed by their Creator," and the utilitarianism of what follows, somewhat in tension.
After arguing that men are endowed by their Creator with rights, and that governments exist to secure those rights, which in itself creates a right to revolution, they than back off that truly radical concept in two ways.
First, they note most of the time as a factual matter, people put up with a lot of stuff, and so practice and the bloody prudence of revolutions means that you don't want such things willy-nilly.
Second and more to the point here as to Ryan, the Founders then also argue that if rights have divine sanction in some sense, then in practice what is effective is what should be adopted (...as to them shall seem most likely to effect their Safety and Happiness).
But to claim that in and of itself to claim that rights have divine or non-human sanction is what makes one a radical in itself reveals you as the radical, not Ryan, whatever other flaws he may have.