You need to look at curable disease to understand why it is difficult to cure cancer(most of them). Unlike infectious disease where we have immune system that works in coordination with external agent(antibiotics) to get rid of the offending agents. In the case of cancer, for cancer to establish one of the essential property other than immortal division is to evade immune system. Most of the times we have cells in our body undergoing dangerous mutation, our body is equipped with multiple checkpoints to prevent the mutation to become cancerous, one of them is tumour suppressor genes (imagine it's like a self destruct button which destroys your cells if hacked ) and the other is immune system. For a cancer to establish it has to bypass both these check points and also establish certain properties like building new vessels, become independent or self sufficient to growth factors( These are like external signals that command cells to multiply). Now basically we have immune system that is either choked or un responsive, so even if we kill majority of cancer cells, small portion of survivors are enough to reestablish cancer. Whereas in infectious disease, our immune system cleans out those remnants even if they survive. Our cancer cells are basically mutated normal cells, so any agent( surgical or chemo) that we use also have potential to harm bystander cells. Basically we need to balance reducing tumour loss against the possible toxicity of these agents. This makes treatment more difficult compared to antibiotics in infectious disease. There is another problem of diversity within the cancer, like it is responsive to chemo agent in one person but isn't in another. All these problems make treatment of cancer virtually difficult.