As a guess, I'd say it's because the glucose can be used by the cancer directly as an energy source, and that the fructose can either be metabolized in the tumor directly as an adaptation, or it ties up resources elsewhere in the body that could have been better used to fight the cancer.

The lack of protein or fat in the juice means that it cannot help the rest of the body rebuild itself as the tumor is sucking up all available resources. Shipments of essential fats or amino acids are being hijacked by piratical cancer cells, and never reach their intended destinations. If there were an oversupply, some might still get through.