Transplanted organ rejection occurs when the cellular community detects other cells that are different from themselves, and attack the newcomers, even though this action will eventually cause their own demise. Let's take this further. Subatomic particles can be divided into smaller and smaller groups. Analyzing the principle from the other perspective, we can see that it works in the same manner. Every human is a part of the human race.
Humanity is then part of the animal kingdom, and subsequently, all living things on Earth.
An imaginary scenario may make this clearer. Imagine the Earth is actually one of nine electrons orbiting a nucleus, which is the Sun. Our atom, the solar system, is then part of a molecule which, together with all the other atoms and molecules in our galaxy, make up an object. Even with the ability to travel between galaxies, we would still only see the parts, and never know what the parts create. The distance between particles seems incredible to us, but distance is relative to size.