So, let's back off from the previous answer and focus just on Wittgenstein, and just on language.
Wittgenstein gives a good argument that language holds itself together through 'games' that allow individuals to determine meaning by choosing usage, taking agency to deploy it, and getting pushback from the other agents involved.
Meaning, usage, and agency are three entirely separate but interdependent things, and no one of them can be entirely explained by any combination of the other two. (That is, other than the totality of all of those plus all the rest of itself, a collection which is infinite in both content and detail.)
Wittgenstein himself was focussed on Logical Positivism, so he emphasized the degree to which meaning and usage are circularly dependent, and yet not complementary. So you cannot determine either from the other; neither is directly traceable to the other; nor is one the absolute product of the other, because there is a third component present.
So, you cannot answer How questions entirely in terms of Who/What/When questions or the reverse. Without actual engagement and negotiation, it is impossible to learn rules correctly by observation. And one cannot communicate an abstract underlying picture of the world through surface behavior, corresponding internal models have to arise in the person being taught, and then they have to be shaped through interaction. (This is the early Wittgenstein's 'ladder' analogy - at crucial points in the learning process, we cannot deliver the most important concept, we have to provide a ladder up to it, which is partially fiction, and will be discarded as misleading when the necessary foothold appears). This destroys the notion of a single recordable kind of truth in terms of direct facts, and derails the LP enterprise.
Your question is the same question as LP was asking, only about How and Why questions. The whole structure is symmetric, so you can just complete the remaining analysis by parallels.
The argument instead of 'LP fails', is basically, 'B.F. Skinner fails'. You cannot determine actual motivation entirely from behavior. You have to guess the internal furniture of the individual's worldview, and you can't. The information is incomplete and we are not psychic.
To the extent you can actually relate, the internal structure of meaning is basically impossible to put into a usable form, even with their participation. So there are Why questions about this person that you can never answer with How answers unless you have his whole library of associations. This is not just history, but the internal idiosyncratic framework of reasoning and symbology that the first arm of the argument says we cannot determine.
So even if you have all the How answers, you would have to guess all the What answers to answer many Why questions. Just the way the primary argument shows LP cannot be done, this cannot either.
If this does not work in just one part of experience, language, it does not work at all. But the same analysis and principles apply far beyond language.
As for the edit. What science exists -- what questions we do and do not have answers for -- is determined by 'why' questions. So, in order to choose where and when to study what phenomena, scientists must answer 'why' questions. Sciences do not ask or answer pointless questions as a matter of course. People will only devote their resources to questions that inspire in them some sense of meaning.
Also, in choosing axioms and paradigms, science anchors itself in metaphysics -- only the models that are blessed by a current paradigm are going to mean quite the same things to current working scientists in a domain. So during periods of revolutionary science, or of initial paradigm formation, science also falls back on philosophical answers to 'why' questions, and turns them from mere insights into solid models usable by real people.
Things like Everett's Many-worlds model, or the Copenhagen rules are oversimplified metaphysics that help ground the concepts of quantum physics.
So are the notions of a light 'wave' or an 'elementary particle'. But they make up a body of metaphors that allow people to get traction so that they can be inducted into the paradigm. They played major roles in the evolution of the science during the paradigm shift from classical to quantum mechanics. But as science, they are actually meaningless. They are neither testable, nor quantitative. They give us a metaphorical framework of 'why' answers on which all the real, scientific 'how' answers will be built.
The same kind of thing can be said for the concepts of line, point, etc. from Euclid, or of set and function. We capture the metaphor in axioms, at which point all of it becomes actual math. But we retain the metaphor itself, which is by nature a metaphysical, ontological or epistemological theory simplified for everyday use.