I want to ask a question.
The opposite of "must" is "must not", everybody knows.
But, what does "must not" mean?
Does it mean that you "may choose to do or not do" or you "may not choose to do"?
Or it depends on the situation?
As must expresses obligation, so must not expresses prohibition.
In answer to your question, you must not means you do not have the permission or rights to do whatever. This is equivalent to your second alternative: "you may not choose to do".
Hence, you must not does not mean your first alternative "you may choose to do or not do".
This is confusing to German learners of English in particular because the German verb müssen behaves differently from the English must, whereby "du musst nicht" does indeed mean "you may choose to do or not do".
For example:
Du musst nicht gehen
does not mean "You must not go".
It means "you don't have to go; you may choose to go or not to go."
Note: This answer is a simplistic account of just one of the functions of the complex English modal must.
If you must do something, it means there is a breath of urgency in that statement. If something must be done, then there usually follows an immediate consequence. The same follows for things that must not be done. Consequence for things that must not be done follows when something is not omitted from the action. Therefore if someone must not speak in public and instead speaks in public, a consequence may follow (which is often immediate in nature); however, it might not. Which makes this statement a rather dramatic one -- while also urgent; however, in most cases when something must or must not be done, a consequence does follow due to reason the person used "must" rather than "should." Should holds a potential consequence as well, yet that consequence may not be as immediate. Should is often used in philosophy when must is often used in upholding a law that has a severe punishment.
"Must not" means it is urgent, that something is prohibited to be done. It should prevent you from doing anything. If prohibition is not urgent, then you can use "need not."
VP
means 'It is necessary/obligatory that notVP
', i.e, don't doVP
. That's because the modal is outside the negative scope. Since must is a modal, it has a paraphrase: have toVP
(always pronounced with an /f/, never a /v/), which means the same as must in the affirmative, but has the opposite meaning in the negative. Not have toVP
means 'It is not necessary/obligatory thatVP
, i.e, there's no obligation to doVP
, because here the negative is outside the modal.