That's painting things with a pretty broad brush, not everyone thinks this way. From conversing with people about the issue, those that do, do so mostly because they haven't actually put any conscious thought into it, even a few minutes is enough to knock down that straw man.
Personally, I think humans are superior to other animals because we are more capable of feeling and thinking than they are. A bacterium or plant cannot feel joy, it cannot communicate pride in it's accomplishments to other members of its species, it cannot feel pain, it cannot suffer, it cannot develop into an adult which can do those things, it just is. A pig, dog, or dolphin can do many of those things, a chicken or fish can a little but much less so.
Empirically, to me, this capability criteria sets a 'value' roughly proportional to their number of cortical neurons on a logarithmic scale.