http://www.theatlantic.com/magazine/archive/2002/09/a-primer...
I was actually almost involved in one of such cases, I haven't invented it out of the thin air. If you can't imagine such a scenario happening to you, you're of course lucky and you'd like to use one private key for everything. But the scenario is real.
The equivalent when the scenario is an attack, and not a legal game: some entity manages to hack your computer with which you access the service A and on which you have only the private key for A, but not your another computer with which you access the service B, with the another key.
Separate keys: just your access to the service A is compromised, one key: all accesses are compromised at once.
The real goal is privacy, given that your public key is available on github and sent via plaintext when authenticating.
There are some added benefits to managing separate ssh keys for each server: it forces you to use tools to manage your keys, which make it easier to mitigate disaster when the time comes to rotate your keys due to compromise.
Just imagine that somebody can request from you the ssh key to just one of the services you access. Then he gets the access to all of them.