I think part of the reason many of us (especially the non-religious users) find the idea that we can learn from evil and suffering abhorrent is because we are still clinging to the idea that "diabolical evil" is something that shouldn't exist and should be destroyed. If something that shouldn't exist can be useful - because we can learn from it - then it becomes hard to argue that we should get rid of it.
To use a random example: the Zika virus in Brazil causes severe birth defects in babies if their mothers catch it while pregnant. What could we possibly learn from this? ...Actually quite a lot:
- Biologically: we can see how viruses evolve, how they spread via mosquitoes, how it affects the development of the foetus etc.
- Society: in recent decades people have learned to be far more accepting of disabled people. If people are more accepting perhaps there will be fewer abortions.
- Personally: parents learn that having a disabled child is not in the end of the world and that they can still bring a lot of joy into their lives.
- Medically: if we can learn what causes the birth defects then perhaps we can also learn how to cure it.
But maybe that last part is debatable... if there are so many potential benefits to the virus, then why would we want to get rid of it?
Even if we do get rid of it - how? Do we destroy the virus? Destroy the mosquito that carries the virus? Destroy the forests the mosquitoes that carry the virus live in? That last part might sound a bit extreme, but keep in mind that building hospitals and day centres and special needs schools (all of which the affected babies and parents will need because of that damned virus) often destroys large parts of the environment.
So - the virus itself (potentially) has a lot of upsides whereas fighting the virus (again, potentially) has a lot of downsides. How then can we argue that the virus is evil e.g. shouldn't exist, and the only way to deal with evil is to get rid of it?