Your analogy is flawed.
Assume for the sake of argument that hundreds of puppies are adopted every year, while only a few are euthanized (in reality, the numbers are about even). In that case, is focusing on the euthanization more "relevant?"
How much of the "bad news" we hear focuses on exceptions rather than rules? On small fractions of a population or category rather than the whole?
"...this problem has been exaggerated and sensationalized, it's not as bad as you've been led to believe" is true of almost every damn story you hear in the media.