A certain irreducible background incidence of cancer is to be expected regardless of circumstances: mutations can never be absolutely avoided, because they are an inescapable consequence of fundamental limitations on the accuracy of DNA replication, as discussed in Chapter 5.
Of course mutations can be completely avoided. DNA is digital information, which can be copied perfectly. Whether any particular living organism actually does so is another matter, and likely one of the issues that need to be adjusted. Not that it really matters: cancer is actually pretty simple to treat (just kill all of the malfunctioning cells), is only a problem due to the limited accuracy of the knifes we can currently wield, and with nanotechnology and robotics advancing at geometric rate will likely fall within a century to fleets of medical micro-killbots.
In any case, we need to decouple our minds from our bodies at some point. The only place our current physical forms are at home is Earth. Furthermore, while our brains are impressive their inherent biases are worse and worse fit for modern circumstances, and most of their power is not easily accessible to consciousness. We must figure out how to transfer that consciousness from one physical shell to another. That way, we can inhabit human bodies when appropriate, move to supercomputer cluster to do physics, become a spaceship to set up a space colony in outer solar system, and make that colony itself a vast virtual world with high-power transmitters for moving people in and out - much more efficient than building a metal shell filled with oxygenating gasses. And as a nice side effect, it moves cancer from a killer to "damn, ruined my clothes" status.
If a human could live long enough, it is inevitable that at least one of his or her cells would eventually accumulate a set of mutations sufficient for cancer to develop.
That is a tautology: if you live long enough for event X to happen, then it's inevitable that X happens, since if it doesn't, then you haven't lived long enough yet. You can replace "cancer" with "every atom in your body randomly undergoing cold fusion into iron at the same time" and your statement will still be just as true - and just as meaningless - as before.