The theoretical problem with speciesism is that there is no such thing as a species. The traditional proposed equivalence relation of "ability to interbreed" doesn't work because it isn't transitive: every organism would satisfy this relation with respect to its parents, but we have common ancestors with a squid if you just go far enough back. Every animal (and plant, etc...) on Earth is basically part of a single ring species, except that the "rings" of our species are only clear if you picture them arcing through space-time instead of just space. While the ethical status of individuals must have something to do with their biology, there doesn't seem to be anywhere we can put a bright non-arbitrary cutoff line for that status.

The practical problem with speciesism is that we may soon be getting a lot more "species" to worry about, and it would be good to have an appropriate ethical framework for that ahead of time. What kind of modifications can we give to ourselves or our kids before their "post-human interests" lose importance relative to the unmodified? How much more intelligence can we give to our domesticated animals before we should start feeling concern about treating them like slaves? What if general artificial intelligences start passing Turing tests without any underlying biology at all? Does it matter if their instructions are a priori vs emulations of copied biological brains?

From an intuitive perspective, it seems obvious that human interests are more important than chimp interests, which are more important than pig interests, which are more important than fish interests... but at that point I get stuck, because I don't see how we quantify "how much more important", robustly, as the categories start to proliferate and blur.

From an outside perspective, the non-superficial analogy to racism is simple: the human intuitive perspective on ethics is lousy, often leads us to atrocious behavior that we and our descendants regret for generations, and ought to be supplemented by something more reliable if possible.

There's a qualitative difference between humans and other animals and that difference is due to language.

It isn't due to language. The difference you describe is based on imagination and the ability to understand future consequences. We wouldn't consider a moral difference between those examples and cases where the subject was able to arrive at the same understanding based off observation, reasoning or memories of past experiences. Language is relevant in only in as much as it is one of the ways that people can arrive at the models of reality and understanding of the future that we consider important.

I might sacrifice a chimp to save the life of a human, but it is a sacrifice, the lesser of two evils, no better than sacrificing a mentally handicapped human.

I would consider it a sacrifice as well and I do care more about humans than other animals.

Much like if I have to choose who the trolley runs over I prefer it be a random cute young girl to my cute little young sister, I prefer it run over the chimp rather than the human.

Agreed. But there are many less-destructive ways of promoting this bias. Far better to become a vegetarian. If you aren't, then I don't think you're entitled to write that letter to Scientific American on that basis.

It is not remotely reasonable to declare people not entitled to write letters discouraging abusive treatment of chimpanzees because they happen to eat meat. People are not obliged to care about all animals equally. Caring a lot about chimpanzees perhaps means you should be a non-chimp-eater, not a vegetarian. Even then it is not at all inconsistent to have a moral aversion to ongoing painful treatment of a creature while considering it ok to breed the same creature for food.

The replies to the arguments opposing chimp testing haven’t tried to show why the defense of such testing is right from a nonspeciesist viewpoint. Rather, they’ve assumed that viewpoint.

Explaining all the arguments against the idea that speciesism is wrong would require lots of space. So I’ll just say here that if we are concerned with wellbeing it is arbitrary to take into account only some of them simply because they are possessed by certain individuals, rather than other ones. Of course many people are arbitrary, and found their moral views on such arbitrariness. But that isn’t really the approach that someone who’s aiming at getting rid of bias should accept.

The main argument that has been provided here in favour for this arbitrariness seems to be: “Don’t you eat animals too?”

I don’t eat animals, and I certainly agree that promoting vegetarianism is a crucial way to question speciesism. But asking whether one is vegetarian or not is not a reply to the problem we’re dealing here. I've met people who just didn't have the willpower to change their food habits even though they agreed speciesism is wrong. I think it's obvious that those who oppose speciesism should encourage those people to do things that reduce the impact speciesism has (such as writing a letter to Scientific American).

There are many people who do things I don't consider right, that's not a reason for me to say they aren't entitled to do good things because that would contradict their previous wrong doing.