Since for me moral demands necessarily flow from human psychology, I don't think we can be obliged to do something that we are not motivated in any way to do. In other words, I'm an "internalist" about morality.
If I drive my car to the store, those carbon molecules that are emitted actually get into the atmosphere circulation systems and affect climate in a global basis. This is shocking, this is amazing! No one in the 18th Century would have believed that anything like this were at all possible and I don't think we have, as part of our common sense, morality, norms and values that are really responsive to those kinds of issues, to the kind of power that we now are able to exert over the future and over people who live very far from us.
I think the mother of all arguments against eating meat now is the climate change argument. Methane is a much more powerful greenhouse gas than carbon dioxide and when we eat meat we wipe away many of the good things that we do when we try to create greener and more sustainable practices in the rest of our lives. So if you add the concern for climate change with other concerns that were there. I think the case for vegetarianism is pretty overwhelming.
I think the challenge of climate change in particular is the challenge for us to create and produce new norms for a new kind of world. And that's why I think as important as the issue of climate change is, it's even more important than it seems because if we can't evolve very quickly, new norms to deal with issues like climate change, we're not going to be able to survive in the kind of world we've created. So I think, really, the whole nature of democracy, of governance, of global community and of solving the kinds of problems of the 21st Century are really at stake.
The problem is that for almost any feature of humanity that you can name, whether it's the ability to suffer, whether it's the capacity to reason, whether it's having lives that can go better or worse, there are at least some other non-human animals that have all of these features as well. So to exclude non-human animals from the range of moral concern but to include all humans, just seems morally arbitrary.
Most "process" philosophy is historicist (e.g., Hegel) and not concerned with "deep time." Maybe Whitehead is an exception. He may be a really important philosopher for all I know. I've never been able to read him.