I think Muzzles saw that there are some possible things to worry about in life, such as the economy, spread of wealth, overpopulation, disease and lack of work.
But, he saw that cancer can in some way, even if in a way not entirely thought through, can link to all of these.
And he put the solution down to cancer.
I think it's a case of Muzzles seeing one thing and then an effect, but not realising that it wasn't the cause.
Correct me if Im wrong (I may be thinking of something else)
But every time we find a "cure" for cancer, it changes so it wont be killed off.
We've not found a "cure" as such in any regards.
We have numerous treatments, such as many drugs in chemotherapy, and then radition techniques in radiotherapy, and more.
In many cases they can cause cancer to recede, or to be destroyed entirely, or they can slow down the growth, or they have no effect.
There's no real cure, since a cure would suggest something that gets rid of cancer and prevents it from coming back. Which even if you lose cancer, it can still return.
There are many treatments however, but cancer is so varied and the people who get it are so varied, and the scenario around the cancer are so varied, that it's very difficult to ensure that one treatment will work for every case.