It's like saying I have a conflict with my wristwatch or my computer. They are things I own. There may be regulations about what I can do with my computer. I can't throw it out the window and hit someone on the head with it. Animals don't have rights, humans do.
Humans have the right of property and animals are property.
It's a Judo-Christian notion. Our ideas of animals go back to people like Thomas Aquinas and Decorates. Descartes was not a priest, but he was still a sycophant for the Roman Catholic Church. His view was that we could do what we wanted with animals because they didn't have souls. He believed animals weren't conscious or sentient because they didn't use language and they didn't have souls.