Why is rabies incurable?
This is because rabies is a viral infection of nervous tissue that propagates through peripheral nerves into the brain and causes brain tissue inflammation (encephalitis).

As long as the virus is in the brain there is no way to get rid of it. The main trade-off here is that everything that would kill the virus will be as (or even more) aggressive against the brain tissue, and impairment of the latter will lead to really heavy deficits in vital functions like breathing and thermoregulation.

The first manifestations of rabies are those due to brain damage. This means, the virus is already there and the brain is already fatally damaged.