Our whole society is based on animals not having rights.
Some people see a gradation where we could have criteria to determine how many rights could each kind of animal have, and argue about small details. But of course the other point of view will be that any fissuring of the concept of animals as "things" will break the dam and there will be no going back.
For anyone seeing simple and clear lines that could be drawn, try to classify the elephants in the article, the differnt kind monkeys, pigs, cows, dogs , racoons and ant colonies. You see the wall that rises the minute elephants get special rights while cows keep feeding us, for instance.