The text of the document is surprisingly brief and incredibly well-edited, especially when you consider that it was written not just by committee, but by a committee of committees from around the world. For having (presumably) suffered at the hand of so many authors, it is an incredibly simple, even elegant declaration.

One of the most reassuring things about humanity is that we try to make things like this. One of the most terrifying things about humanity is that there are those who would find fault with it. There is of course much more on the Declaration at Wikipedia, but the most compelling related resource, to me, was the Declaration on Great Apes. From the preamble:

We demand the extension of the community of equals to include all great apes: human beings, chimpanzees, bonobos, gorillas and orang-utans.

Shades of "Ape Shall Not Kill Ape". Hmm.