This is just my 2 pence worth
If you define 'Cured' as able to lead a normal life then animal research
has cured human diseases e.g epilepsy.
Since we share diseases with animals (cats and dogs have epilepsy, pigs and dogs can be diabetics, pigs can get surnburn and skin cancer. Higher primates get the flu and the common cold, therefore research on the above diseases is not only good for the animals but good for us.
I also have a personal reason for wanting animal research because my wife life has been saved due to drugs which have been tested on animals
Your point about there being more diabetics since the discovery of insulin is not true. It is like saying that we have had more floods in this country since T Blair was elected PM. Therefore T Blair has caused the floods.