The link worked, the premise of "animal rights" is what doesn't work.

This statement was at your link, and helps illustrate my point: Do the folks who respond to [Sierra Club] polar bear cub campaigns understand that species preservation can be cruel—and that saving the environment has little to do with animal rights?

I don't recognize this author's name, but I haven't read much environmental philosophy lately. I'll have to look him up, see if he has been dabbling in theory.

You asked Rights are determined by human consensus, so why can't we all agree that they do?

I think you can see the flaw in this idea by simply looking at the question. We won't agree and you probably could never codify this to the extent you suggest. And frankly, if you are issuing rights to animals along the lines of those granted to children or adults with diminished capacity, then you get into the emotions of their caretakers who would "speak for the animals" in a manner that doesn't fit the way rights might actually have been intended. Cultures vary, what is important varies. Some cultures have dogs as pets, others have them as dinner. Animal cruelty laws are different than animal rights laws, but those are laws regarding the treatment of chattel, property. The fact that protections for horses pulling carriages came into existence before the laws regarding the treatment of children is an interesting illustration in the history of the expansion of human rights under the guise of animal cruelty.

SRS