So-called "speciesism", a neologism coined to capitalize on the stigma attached to racism and sexism, is a shibboleth among animal-rights extremists, a self-exculpatory flag under which to attack humanity.
But what is the opposite of "speciesism"? We should have a name, it seems, for those who
think humans do not possess any morally unique qualities and people are no better than other lifeforms. They argue that those who claim a special or a higher status for humans are no better than those who talk about racial or male superiority.
Fortunately, there is no need to coin a word. The opposite of speciesism is already named, and its name is bestiality.
The denial of human primacy, "the assumption that it is wrong to prioritise humans over animals", is of a more refined sort than that of a rural zoophiliac near a livestock farm; it is a kind of Platonic idealization of bestiality, where the human gives over not mere bodily fluids but the mind's own capacities of affection and persuasion.
Worse still is the Gaia theory which, having escaped its creator, posits a sentient Earth or -- just as wrongly -- a planet or ecology with value beyond that of its constituent parts [see also here]. The adherents to such theories have not only embraced bestiality, but they pathetically imagine that they will be thanked or loved in return.
[Update 11 September: related thoughts from Richard Fernandez.]