It's the only group (or any product of it) where addition and substraction seen as a binary (that is, $- = + \circ (Id, i)$ where $i$ is the inverse map) actually coincides. Note that this also means that it's the only group where $-$ is actually associative.

Edit after Emil's comment (so my answer is not really good then): It's a group (or any product of it) where addition and substraction seen as a binary (that is, $- = + \circ (Id, i)$ where $i$ is the inverse map) actually coincides. Note that this also means that it's a group where $-$ is actually associative.