[Abbreviated argument.]

In the most pragmatic terms possible, this is why throwing more stigmatized groups under the bus is an inherently self-defeating strategy. As long as society has a category of “okay to abuse. Okay to hurt,” devalued, sentient beings are at risk of being demoted into it. When that isn’t challenged on all fronts, the prison just keeps getting bigger. 

So I’m going to be a bit pedantic but I hope my larger point gets across in this stream of consciousness.

If I understood, your fundamental assertion is that human animals are subjected to a legal system they did not agree to be bound by and have no recourse against. This parallels the way humans used to inflict their legal system on other animals. I agree.

I disagree with some of your intermediate points. My impression is that you're trying to dedicate your energy to fixing a whole range of important things that are systemically broken, though, so I'll try to keep this short.  

Hierarchy is not the problem. Hierarchy is simply a way of making comparisons between like and unlike things. We will always need to do that because there will always be like and unlike things needing comparison. After all, you wouldn’t want to eat a steel pellet even if it looked like a grape and you wouldn’t get very far expecting a pig to respond to questions in your human language.

When I criticize hierarchy, I mean that disrespect is a problem; and believing you have more of a right to be treated like you matter than someone who doesn't have a particular, socially valued trait is wrong. Acknowledging that other sentient beings have as much right to be living their life as you have to be living yours should be the default. 

Humans understand none of the languages that other animals use to communicate. Currently, we can neither pose questions to them nor understand their answers, and we blame this shortcoming on them.

Anthropology made an ass of itself for a long time by asserting all sorts of racist, incorrect things about foreign human languages, thanks to its assumption that native peoples must be simple and primitive. I expect that at some point it will become plain that biology does the same thing. It went through a phase of half-heartedly trying to get animals to speak human languages, but after it turned out that animals could prove their intelligence in human terms, further studies were not done. Humans have managed to communicate imperfectly with apes, dolphins, and African gray parrots, that I know of, and always by making the animal learn a human language. 

For example, it seems obviously ridiculous to people living in the age of Tumblr for us to, say, put pigs on trial in human courts, but that’s exactly what Europeans did for a very long time:

That actually isn't news to me. And things haven't changed so much - animals who injure or kill humans are routinely executed. It's just not called execution anymore. This is also glossing over the multitudes of wild animals who are killed (or more rarely, relocated) for existing in a location that is inconvenient to humans, and the millions of cats and dogs who are killed for not having a human owner.

And while it may seem obvious to us now that the reason for this probably has something to do with the fact that pigs can’t speak in human languages or hire lawyers, I find it hard to believe that most people living in September of 1379 were ignorant of those specific facts, y’know?

Yes. Which is exactly why animals had those rights on paper, while slaves and women didn't: animals weren't going to press their own defense in an arcane,  human-created system that they didn't understand or even know existed.

We still have a system of crime and punishment that punished some more than others. We still have a system of law that most of never agreed to and that we have no recourse against. After all, to what court other than a government one can you appeal for redress of grievances against the government’s own laws? And still, that part doesn’t seem insane to most people, even though by all reasonable accounts it is a farcical apparition of “justice.” Even that article I linked doesn’t call criminal “justice” systems insane. To that author, only putting non-human animals on trial is insane. Putting human animals on trial in an equivalent way today as we did then? Why, that’s just par for the course, all the way to 2014!

This is one of the critical problems facing us now - and you're completely right, almost no one is addressing it.

So. That’s weird.

Especially for a people whose founding national principles are fairness and freedom from tyrannical rule.

The founding myths of any country have precious little to do with how it actually functions. The ruling classes encourage most people to believe in things that are incorrect and actively harmful to them.

TL;DR: The hierarchy of “human versus non-human” is not inherently bad—it can’t be, because it’s irrefutably true—but when we consider the actual history of how that distinction has been applied, what we find is that we are not only much more similar to pigs than we would have thought, we are also treated much more like we once treated pigs than we ever imagined.

And that? Well, that would certainly seem to be cause for concern for everyone who still believes humanity has “progressed” beyond those “barabric” times. Just sayin’.

I think the hierarchy - if you're talking about a presupposition that human interests should be prioritized over animal interests in all respects, and doing so is morally correct - is inherently bad. If you're observing that humans and animals communicate on a pathetically basic level and therefore treating animals "the same" as humans wouldn't address most of their actual problems, we're in agreement. Either way, I think your observations about humans' treatment in the criminal justice system are entirely on target.