Raz’s theory is that interests justify rights and rights justify duties.
But whether there are duties or not depends on factors that are independent of a person’s interests. My interest in receiving an education is the same whether the people in my society can afford it or not. If they have to chose between education and eating, they might well have no duty to build schools, even though I have a strong interest in receiving an education.
Raz tries to get around this difficulty by distinguishing between general rights, which do not logically entail the existence of corresponding duties, and particular rights, which do entail corresponding duties. But since he also holds that rights are sufficient to justify holding others under duties, it is hard to see how he can call general rights rights. (see Raz, pp. 211-212)
Note: Raz and Hart do not mean the same thing by “general rights.” Sorry.
This raises a broader problem: what do rights do in Raz’s theory? For example, why couldn’t we just replace them with very important interests that can be protected by holding others under duties? If we can make that replacement without losing anything important, then it seems that Raz’s theory does not actually explain what is distinctive about rights, that is, what rights do that other moral concepts do not.
I passed out a short article critical of Raz's theory in class. I think that the criticism is, basically, the point we made about general rights.
If you're interested but weren't there, you can find it on JSTOR. The citation is: Margaret Holmgren, “Raz on Rights” Mind 94 (Oct., 1985): 591-5.
Questions and answers
In the end, I think that Hart and Raz are really trying to answer two different questions.
Hart’s question is “what is distinctive about rights?” His answer is: they give those who have them control over others’ freedom.
Raz’s question is “what feature do all rights share?” His answer is: they protect interests by imposing duties on others.