I'm also not really following your point here. We may treat a braindead human better than a chimp, but the anti-speciesist would say this is not justifiable.

Is there a definition you find better?

The definition you are describing is weak because it doesn't imply any particular moral implications, not that it is a bad definition.

An anti-speciesist does not say this is not justifiable because this weak definition of anti-speciesism doesn't imply any particular moral reasoning, just that the arbitrary discrimination based only on membership in a species is not justified. If the moral justification for treating a braindead human differently from a chimp does not discriminate based solely on species, then an anti-speciesist has nothing to say about it.

I'm not really following. Do you have an example of what you mean?

There are two different questions here. What do we, and what should we?

Do you think that is an arbitrary distinction to make? That valuing the life of a chimp over a blade of grass is an unjustified bias?

Since this is a weak anti-speciesism, those who wish to use it to achieve a particular aim must rely upon the moral reasonings of those who they are trying to influence. These moral reasonings are often problematic in their lack of sophistication and rely upon an unsophisticated application of anti-speciesism.

The lack of sophistication of common morality is evident when the moral justifications people provide clearly contradict simple edge cases like the brain dead or infants.

Applying anti-speciesism to these unsophisticated moral systems is also problematic; take the issue of 'suffering' as being an important basis for discriminating between organisms and one's moral responsibility. We have nothing but a highly subjective, biased definition of suffering. How do we know that a blade of grass doesn't suffer? Because the behavior we see from the grass is not emotionally relatable because it doesn't mimic human behavior when humans appear to suffer.

This quickly becomes a very thorny philosophical situation, but anti-speciesist proponents don't seem all that eager to actually explore it. It seems that they don't want to actually pursue the full implications of anti-speciesism, just move the line to include more charismatic animals.