Human Exceptionalism
Human Exceptionalism is the latest term to buzz around to describe the phenomenon of human supremacy. It is a clever term I would say, as it doesn't have the bigot aura that supremacist carries. But in essence it means the same thing even if its users deny it.
Exceptionalism suggests uniqueness. Many animal righton arguments seek to downplay human uniqueness and trivialize it in order to boost the moral position of nonhumans. Exceptionalism counters that human uniqueness is real and significant.