I am also at a loss to explain how anyone who has had personal experience with the ravages of cancer could pose such a question with a straight face.
Statistically, almost everyone will know someone who's died of cancer. I know I do. And chances are, it's going to be someone close. But it IS perfectly possible to compartmentalise personal feelings and experience from a wider theoretical proposition and consider the proposition from a different perspective. It's only by testing our beliefs from various perspectives that we can be sure they're correct.
All that matters is curing the present ailment.
Well, let's take this further... Why?
I suspect the core of your answer, if phrased in rational terms and stripped of emotional language, would be something like "to reduce the net suffering of humanity because reducing suffering is in itself a goal that is good".
Leaving aside issues of what is good, and accepting the answer on its own terms, there is still a problem. The counter-proposition would be that actually one can reduce net suffering to the most people by not curing, for all the possible reasons outlined above. As I said, this can't be calculated fully, but can be extensively theorised and extrapolated, which is why I would consider it a wicked problem and so we have to default to a pre-existing ethical framework rather than a rational analysis.
The ethical framework allows us bypass the rational analysis and short-circuit the problem, but is does not answer it. It just redefines it into non-existence.
In essence, the argument we use to try to cure cancer is NOT "to reduce global suffering" because we can't ever KNOW that would be a true outcome. Instead we choose to try to cure it because we redefine it to be either "reduce this individual's PRESENT suffering" (in the case of an active episode) or "because curing cancer itself, regardless of known outcome, should be a good" (in the case of preventive measure). This is something that I think is a redefinition that both of us could sign up to. I think
T'Baio also could, because it allows for fairly neat bypass to his argument. Of course, as more data arrives, the equation may change, so we should be open to recalculation.
By the way, your analogy of the fireman/burning building is not a good one - you say that the counter-proposition for saving a life in that setting is uncertain potential for that one saved life to become a serial killer. But this misses the point here, which is about whether the outcome can be
predicted and meaningfully theorised about. In this case, the statistical chance of the baby growing up to be a serial killer (or even more widely, a "bad person who increases net suffering") cannot be calculated by the fireman within the timeframe he has for making the decision. Therefore it is entirely right that the baby be saved, since without any ability to calculate the future outcome, the argument condenses into a much simpler one: save a life or not.
Deciding whether to trying to cure cancer is a more long-term question, involving decisions regarding funding, allocation of resources and depriving other areas of resources. Calculations & projections can be made of all of these issues, and many others. The calculations all have significant margins of errors and are often at best "guesstimates". But crucially - and this is the key difference - the guesstimates are not wholly without merit and therefore have to be taken into account when calculating net benefit or harm. The unpredictability/uncertainty but not total lack of merit, is precisely why the problem is wicked, whereas the more finite problem of the fireman/baby is not wicked but completely solvable (or if you prefer, completely insolvable) and in that technical sense, trivial.
(this of course leaves aside other ethical duties, such as the fireman's duty to do the job he is contracted to do, etc, etc, etc as they're not really central to the argument you presented and why you presented it.)