The body has a relatively easy time finding and destroying cells that don’t look like your own. Cancer consists of your own cell gone aberrant, multiplying without control, ignoring death signals and/or disregarding tissue integrity completely. All of these factors make them incredibly hard to kill for your own immune system. Another person’s immune system would, however, still recognize them as foreign and destroy them swiftly.
Though I would like to put one of your assumptions into perspective: Everyday your body kills thousands of unstable, old or dysfunctional cells that could run risk of developing cancerous patterns. What we colloquially call cancer in a clinical context is basically the terminal stage after a million fail-safes and statistical improbabilities have been exhausted.
The worldwide average age for a first-time cancer diagnosis is somewhere between 55 and 65. Considering visible cancer to be the absolute end-stage of this disease, that means an argument can be made for cancer actually not spreading easily or quickly at all (until it does).
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