I don't wish to belabor this point, but I think the quote from Bernard Williams in the previous post could use some more unpacking. The view he expresses is not uncommon as a response to the charge of speciesism. Simply put, he accepts that his view is speciesist, but does not see a problem with that. One might say that there's no need to find any justification for a preference in favor of humanity, it's just a brute fact about how we think and how we morally reason.
It's important to remember, however, that humans have often been very wrong on any number of moral issues. This fact is so mundane that I won't even elaborate on it. But this fact also carries the implication that we would be foolish to assume that our present society is correct in all its moral judgments. We must be vigilant in our own reflection and self-criticism, and not take our initial prejudices as the final word on ethical matters.
This relates back to my first post, when I discussed what matters and why philosophy is important. There is a sense in which much of what is important is obvious, and doing what is right is clear. But people often take from this observation that all of ethics is clear, which is false. And if we take seriously the moral progress that has been made in human history, as we should, we should take seriously our place in the moral progress that has yet to take place. This means that we must be very critical of our views, to avoid falling prey to the moral failings of our day.
Williams ascribed to a particular flavor of moral relativism, and this no doubt permeated his moral outlook. If you don't believe that there might be ethical truths that you don't yet grasp, you will likely fail to sufficiently criticize your own beliefs. Many people I've discussed these topics with have ended up proposing some kind of moral relativism in which their speciesism is unobjectionable. But even most of these people do believe in other moral truths, such as the wrongness of racism and sexism. If you think that these are serious charges, and that others should re-evaluate any racist or sexist viewpoints they espouse, then you cannot rationally accept your own unjustified speciesism.