In every case, non-human rights are non reciprocal. To these people, humans are bound to respect and yield to the rights of non humans, but not the other way around.Nor are non humans bound to respect the rights of other non-humans. Sheep may safely graze without fear of a lawsuit, but mowing your lawn could have serious repercussions.
If it weren't for Cass Sunstein types using this as a way to further control people, this would be downright laughable.