For all the talk of excessive individualism, the problem in the world today is not too many individual rights but that individual human rights are not sufficiently respected. States and societies have a variety of claims on individuals and modern states have awesome powers to bring individuals to their knees; if necessary, to break their minds as well as their bodies. Human rights, and particularly legal rights, are among the few resources of individuals in the face of the modern state. The balance is already (always?) tilted against the individual. The only likely result of advocating collective human rights ... is a further strengthening of the forces of repression.
Every day we see individuals crushed by society. Rarely, if ever, do we see society torn apart by the exercise of individual human rights. Social disorder and decay are usually associated with the violation of individual human rights by the state or some other organized segment of society. Human rights are a rare and valuable intellectual and moral resource in the struggle to right the balance between society (and the state) and the individual. Unless we preserve their distinctive character and stand firm on their character as individual rights, their positive role in the struggle for human dignity may be compromised.
I'm not actually big on the misleading (IMO) expression "human dignity", but it'll do as a place marker in this context. I think these paras from Jack Donnelly's book on human rights sum up something important.