Two thoughts:

• You don’t see a reflection in water when you look straight down at it—only when you look at an angle that depends on the refraction index. So when you look at a distant animal in the water and see its reflection below it, that doesn’t mean the animal itself can see that reflection. Like you, they can see the reflections of other animals in the distance, but they can’t normally see their own.

• The reflections animals are used to seeing are always mirrored vertically due to the horizontal orientation of the water surface—the upside-down orientation is probably an intrinsic part of their understanding of what a reflection is. So when they see something mirrored horizontally, it’s missing two of what experience has taught them to be fundamental characteristics of reflections—vertical inversion and an oblique viewing angle.

Hm, just a quick thought. Infant animals do get 'surprised', but just accepts their environment pretty quickly. Adult animals won't get surprised if they see themselves in the water, but they will if there's suddenly a Portal 'mirror', showing them selves, in the middle of no-where.

Exploration of 'self' only happens in safety and waterholes are not safe for predators. I don't think most animals have the opportunity/energy to diverge their attention to reflect on their own reflections, while watching for predators. Maybe Elephants and similar safe animals ?

Edit: I think the issue with shadows are the same. Kids can follow, or be scared of their own shadows, but pretty quickly habituates to it, so its brain doesn't react to it all the time and burn off energy.

Neat question/connection btw.