The reason why is because. And how.
In my opinion, a why-statement should be used to state Why it is that something has come to be. In other words, it should aim to name the cause of an effect.
As alluded to by my example, the preponderance of offense occurs in news item headlines. Annoyance at these demonstrates how I or anyone with housepet peeves is a pragmatist of selective convenience. Notice I said how and not why. I'm more inclined to say pet peeves demonstrate selective intolerance but wanted to point out here that the offense can occur as well in everyday speech, as I would've done had I written "demonstrates why I'm a pragmatist of selective convenience", to which my snide reply would be "Because I'm an asshole".
The following is an example of a micro infraction I read this morning: Why this summer that's actually not one comes at just the right time.
[Here's another pet peeve: you'll have to trust my translation. Our deep translator does not yet offer a proper rendering of the defining relative clause as I have written it and instead offers exclusively versions of a non-defining Why this summer, which is actually not one, comes at just the right time. German grammar makes no distinction without the comma, but I, being a part-time pragmatist, understand that it's the not-being an actual summer aspect that's had a timely arrival, not the summer itself, the latter of which is what the non-defining rendering with the commas would indicate. I'm fully aware the context would provide the clarity to the intended reader, i.e. I know the last several weeks have been cool and rainy and that the inference of "this summer's arrival" alone could preclude anything other than this. But other people read, too. Not everyone's privy to the defining quality of this timely arrival.]
A logical explanation of the why in the above headline should involve an examination that explores the mechanisms that determine the weather in this region of the world and an observation of present conditions that would answer the question Why is the weather like this now? What makes the infraction less flagrant is the strong contextual association of "comes at just the right time" with "is what is needed or desired". The answer is so broadly self-explanatory there need not be a question; we need rain more than fire right now. But I cannot help myself; the why bothers me because I know it lacks an explanation as to why this thing we need now but does not typically occur at this time of year has so mercifully and seemingly coincidently arrived now, of all times.
I've identified a couple levels of irritation that could be split into categories based on the amount the glare each grates: 1) the whys that are all how and 2) the whys that cover both how and why to more and less proportional degrees.
Here's a fun one: Call up an array of news sites and do a page search for why to see if you can guess which category the headline corresponds to. I have to admit that, to its credit, the NYT homepage had at the time of conception no examples of either, only four real whys. [Checking again just now, they have a whopper with cheese.]
I'd like to think there's a real linguist or grammarian or lexicographer somewhere researching the origins of this and cataloguing usage. Advice to myself regarding pet peeves: Go with the flow. Mind the gap.