With humans specifically, a lot of it has to do with dispersal and competitive niche exclusion.

Competitive niche exclusion means that you can't (usually, there are some exceptions) have two species occupying the same biological niche. A niche is a way of making a living...the foods you eat, the places you nest, the times you are active, etc. Other hominids were similar to humans, and modern humans have a very broad niche (we eat a lot of different things, live in a lot of different places, etc).

So it's not surprising that there's no other surviving hominids where humans are...you'd expect us to push them out of their niches. Earlier hominids seem to have narrower niches and so could survive alongside each other in some cases. And often, animal species occupy narrow niches that allow them to avoid competing, for example similar species of fish may specialize in living in different parts of a lake. So you get a lake full of several species of sunfish, for example, where one eats snails on the bottom, another eats bugs in the shoreline plants, and another eats plankton in the middle of the lake.

The other relevant factor is dispersal. Humans are very good at dispersing. Of course, you can fly around the world in a jet today, but even 10000 years ago we had walked or boated almost across the whole planet. And people didn't stop moving once they got to new places, people kept moving around between most of these populations. Most species aren't this good at dispersing, so you get one species here and another similar species there, and you wind up with a bunch of similar species in different parts of the world, originating from isolated populations. People just move around too much for this to happen.

Humans aren't unique, there are other species where there are no other similar animals for various reasons, but this why humans wound up this way.