Really, the entire premise of the Universal Declaration of Human Rights shows that it is an outgrowth of Western culture.
The idea that, as the Declaration says, there needs to be recognition of the
... inherent dignity and of the equal and inalienable rights of all members of the human family
is a Western idea. It first came to prominence during the Renaissance when humanism started to push the idea of human rights. It then was expanded upon during the Enlightenment when thinkers like Locke and Rousseau argued that human beings had various rights that were theirs by virtue of the fact that they were human.
This was an idea that was not nearly as prevalent in any other culture. Therefore, the idea of a document that delineates a set of universal human rights is inherently a Western idea.