modal verbs - negation of "must"

You mustn’t eat it all. [i]
You needn’t eat it all. [ii]

CGEL says “In [i] the negative applies to the eating, not the modal obligation: “It is necessary that you not eat it all”; it is thus internal, within the scope of the modal. In [ii] the negative applies to the obligation: “It isn’t necessary for you to eat it all; here then it is external, outside the scope of the modal.” (The Cambridge Grammar of the English Language, p.176)

For [ii]’s explanation, I’m not confused. But for [i] it’s not easy to understand the explanation, for my native tongue has three ways of negation for the obligation –– applying to eating, or must, or it’s sort of ambiguous. So what I want to know is whether there isn't no arguments against the explanation of [i].

Answer

It might be easier to understand if we use a syntactically simpler action, initially without negation...

1: You must eat (it is necessary that you eat)
2: You need to eat (note that to is grammatically required here)

For most purposes, #1 and #2 are semantically equivalent (it is necessary that you eat). But things change if we introduce negation. There's only one valid way to negate #1...

3: You must not eat (it is necessary that you do not eat)

But there are two ways to negate #2, and they have completely different meanings...

4: You need to not eat
5: You need not eat

In #4 the negation attaches to eat (i.e. - to the activity of eating), so it just means the same as #3 above.
But in #5, the negation attaches to need (i.e. - it's not actually necessary that you do not eat). You can either eat or not eat - it's a matter of personal choice, not constrained by any obligatory need.

Note that although it's perfectly grammatical, and not exactly an "unusual" form, #4 is a far less likely construction than #5. Probably in order to avoid any possible confusion, native speakers tend to use must rather than need in such constructions (or introduce "Do-support" per @hellion's comment below).