"The 'individual' is a liberal theoretical fiction that does not exist in reality."
Um, people exist. They are individuals who live together.
"People exist in complex relationships that cannot just be reduced to an aggregate of individuals."
Aggregate of individuals is all there is; relationships are inside them. You can't point at "society". It's just all of use with our laws and all
"I really do not see how this individualism can be reconciled with truly Catholic social teaching. For example, how can we have any meaningful belief in a common good when we have reduced society to nothing more than a collection of contentless, interchangeable individuals who exist for no other reason than to fulfill their desires?"
You don't except true Catholic social teaching as taught by Pope after Pope (who could it not be infallible via ordinary universal magisterium??) And who is talking about unhappy "interchangeable" people?? That is entirely off topic. You need to seperate these ideas in your mind. The common good is that which is best for the greatest number of individuals in society.
"At any rate, I think natural rights have only ever been adopted into Catholic thought as a means of defending property against socialism."
It doesn't matter about its motive. The Church authoritatively spoke on this. Pius XI said Rerum Novarum solemnly taught these things.
"realize that Pope Leo used the rights discourse as a pragmatic tool for defeating socialism and nothing more."
That's just a red herring. Leo XIII spoke of PRINCIPLES. Saying people have rights is not a matter of speech or a method.
"Now that socialism has been discredited, it seems like it might be a good idea to emphasize the other side of the spectrum to defend against the abuse of property rights and the dangers of vulgar individualism."
Agreed (but don't forget about Obama