The first of these rights listed is Life. Already, we find modern culture at odds with humanities natural rights. Leaving aspects of eternal life (and the sinful denial of it) alone, we see numerous violations of this most basic right in our modern culture. From issues abortion and stem-cell research to the death penalty and euthanasia, the Catholic Church is one of the few organizations in the U.S. to actually stand up for humanity's right to life.
The second is Liberty. I think that people often confuse liberty and anarchy. Sin often tempts people with false claims of liberty, when what it provides is anarchy. Being "free to do what I want" cannot truly happen when bound as a slave to sin. How free is the drug addict or the alcoholic, not to mention those trapped by gluttony, avarice, and sloth? So many "freedoms" espoused by our current culture actually deprive us of liberty.
The last of the three is Pursuit of Happiness (which replaced John Locke's Property). So many people blame the Church for infringing on people's happiness, but how happy are they truly? Look at the famous actors and athletes, the examples of life that our society holds up as an example. How happy are these people? The drug use, divorces, and suicides put to lie the idea of money and fame providing for a happy life. What about Lotto winners? Look up the statistics on how many Lotto winners end up broke, not to mention in therapy, distrustful of family and friends. Only one person can give us the happiness that never runs dry.
"We hold these truths to be self-evident" yet it seems that something is missing. Our society is afraid of the word "sin" because it knows that it sins by even its own standards. We need to find these truths again and show our society the way to achieve them.