Gender dysphoria is a very real and diagnosable disorder, therefore it occurs "naturally" and is not socially imposed. It doesn't matter if it only is detected in humans, it doesn't make it wrong. Source below.
Why could animals not feel in similar ways? We cannot ask them how they feel on the matter, so for all we know it's common. The only real difference is that we (and several species of fish) have the ability to act on it.