What's the difference between なぜ、どうして and なんで when meaning 'why'?

Question

I've been meaning to ask this for a while.

What is the difference between these 3 words. I was taught they all mean "why", but obviously, being different words they convey different nuance and would be used in different situations.

What would be the difference between these 3 sentences and in what situations would they be used?

なぜここにいるのですか？
どうしてここにいるのですか？
なんでここにいるのですか？

Answer 1

From dictionary@goo:

• なぜ is for asking 理由 (reason/motive) and 原因 (cause).

• どうして covers なぜ usage, plus 方法 (method/process). Also, there is additional usage as a strong way to refuse.

• なんで covers なぜ and どうして usage, including the usage as a strong way to refuse.

So I guess どうして and なんで are interchangeable while なぜ has a smaller scope than the two. As for the nuance differences between どうして and なんで, my theory is by looking at the literal meaning of the word, どうして focuses on "how it is done" while なんで focuses on "by what means".

Answer 2

For なぜ:

Very very directly asks for a reason. (Which is why なぜ appears the rudest)

For when you really intend to be direct. "No bullshit, tell me the reason now".

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For どうして:

Deconstructing どうして yields どう(which way/manner) + して(Verb conjunctive form of する)

1. どうする (Which way/manner of doing?)

2. どうして[X]　(Which way/manner of doing did X come to be?) Which is functionally equivalent to "why" since you indirectly ask for a cause of [X]. Also functions as a "how" since you ask for the way/manner of doing it.

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For 何で:

1. 何 (What)

2. で (Instrumental particle)

3. 何で　(By what means) Which is functionally equivalent to "how"

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"how" is a specific concept separate from "why" but share some similarities:

Question: Why? - Type of Response: Reason, Cause, Use of Method(is a subset of Cause)

Question: How? - Type of Response: Method

Simple illustration of the slight overlap:

Why does it work? - It works because this method is being used.

How does it work? - It works through this method.

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Interchangeability:

Following my above assessment of どうして performing both functions of "why" and "how" and 何で for a functionally equivalent "how",

I would say that 何で may be replaced with どうして but どうして may not always be replaced by 何で. (However I do not know enough about the difference in nuance between them.)

None of them does the exact same thing as なぜ though, なぜ's nuance is its directness.