Everyone is unique, in a sense. The real trip-up in that logic is, just because something is one-of-a-kind doesn't mean it has infinite value.

Looked at from one (unreasonable) level, everything is unique. Looked at from another (unreasonable) level, most humans could be replaced with other humans and very little would change.

There's no obvious-to-me level to look from where this argument applies to humans, but not to pet cats and dogs.

Well obviously everyone is unique in that there's only one of any given life, regardless of whether or not anyone's life is qualitatively unique. But it seems obvious (at least to me) that what's much more relevant is that as self-reflective human beings, we have a responsibility to protect other human lives, within reason. Of course, what "within reason" means is a whole subject on it's own.

That "within reason" is the key.