Why are humans so variable in appearance
Because we as humans are really really good at picking up small differences in humans and really really bad at detecting them in anything else.

Animals are often quite good at telling each other apart, far better than humans are, birds in particular are known for this. Just because you as a human are bad at it does not mean they are.

There is a pretty strong evolutionary pressure for humans to be able to tell other humans apart and not much of an advantage for being able to tell two lions apart. We need to be able to tell mates, rivals, relatives, and strangers apart easily. We don't need to differentiating one black bird from another.

We also spend a lot of time around other humans, so we are more familiar with their differences, but the same thing happens to animal researchers whale researchers who spend a lot of time around whales can easily tell two whales apart at a glance. this is also part of the reason some people have trouble telling individuals from a different "race" apart, they are to unfamiliar and uninterested to spot differences. Or the way a car guy can spot the difference between two models at a diffrence but someone else might not.

You see the same effect chimps can tell each other apart but can't tell humans apart, unless they spend a lot of time around humans then they can. They can also match voice to face meaning the can recognize both. 

Then of course you have the fact you are focusing on vision, try to tell two people apart by smell and you will likely fail but a dog will have no problem with it. likewise many monogamous song birds can identify their mates from song along, just as we recognize others by voice, penguins are another example. Humans are very visual creatures so much of our identification ability relies on vision we see the same thing in other visual species, animals tend to use whichever sense are their dominant ones. Saying organisms are more visually similar because organisms with far worse vision than humans can't tell them apart by vision alone is simply an unreasonable conclusion.