I don't think your argument makes sense.

"Justice" and "rights" are human inventions, and only exist insofar as human communities have both the power and the will to uphold them.

In the case of a democracy, the only people who have power are the electorate, and anyone who has some bargaining power over the electorate - for example, children and foreign citizens.

We uphold human "rights" like "freedom" because members of the electorate wants personal liberty for themselves. We like to tell ourselves otherwise, but that's really all it comes down to.

But animals have no bargaining power. So human electorates don't tend to grant them the same rights as they grant themselves.

It's the same reason why most people (despite a vocal opposition) prioritize a woman's "right" to an abortion, rather than a fetus' "right" to life. The fetus is not part of the electorate, and has no bargaining power over the electorate.

That's not to say empathy can't play a role.

Empathy is, after all, one of the reasons why many people are opposed to abortion. And one of the reasons why we uphold similar (although not equal) "rights" for our children who aren't of voting age as we do for our adults.

And empathy is, I think, the entire reason why we uphold the "rights" of many animals. And is why we tend to uphold better "rights" for our favorite animals, like dogs and cats, than we do for the animals we have less empathy for, like fish and insects.

But so ultimately, when people say that animals are "friends not food" out of empathy, I think it makes sense.

But when you claim that animals have "rights", I think you just don't understand what "rights" really are, and how they come to exist in the world.