That's true, the definition of equality can reverse itself. We could consider ourselves animals, just like them. That is also part of the dissonance that happens.
We consider ourselves special, evolved... not mere animals and facing that it might not be true causes dissonance. It can be resolved in very few ways... That we are animals, like them, but at the top of the food chain. Doing to them what they do us justifies it (I can't wait for the dissonance if we meet a superior race that enslaves us...). Others justify their position (God-given, Humans are inherently superior). And others reframe their position, such as being vegetarian or dismissing it from thought.
This brings us back to the inferior part. Under a 'natural' point of view, we are clearly the dominant species. By virtue of this, we have enslaved/kill animals in the trillions, at whim. It may be a heightened form of natural equality. That frames us as "one of them, and therefore equal", but then it is difficult to call that "equal" even so, given our absolute dominance.
The dissonance continues, too. Each version of resolution has additional natural conclusions. If you believe that it is natural to be a predator, then you embrace the notion that the value of life is defined by the difference in power, even in human society. If not, we come face to face with the reality that we do engage in willful violence and 'murder' of animals - and we need a way to discharge that guilt. If we do see them as inferior, we can easily apply it to humans as well. How do we draw the line, why do we draw it? Equality remains a thin line - it certainly isn't "unnatural" to kill our own species, yet now we have the concept of 'human rights'... do you give that up when reducing us to animals? Not so easy to answer, in the end.
It's a hell of a lot of dissonance, and it all stems with the identification with animal life.
