mustn't
/ˈmʌsnt/
phrase
- must not; used to indicate that something is forbidden or, in a tag question, that something is not necessary.
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is “mustn’t” still in use? or is it already outdated? and can I do a question like “must I do something?”
Per my comment, I'd avoid it because it sounds rather dated and "upper class" to me.
Semantically, the reason for avoiding this construction is simply that it takes the focus off the critical word not. Since the "conclusion" clause is intended to convey something along the lines of "I am failing", this negating word is vital to the sense.
In "injunctive" forms, such as "You must/mustn't do that!", the word must is invariably stressed, to emphasise the intended meaning. In OP's usage, the word must wouldn't normally be stressed, because there's no sense of injunction or stricture (except loosely, in the sense that there's a logically enforced conclusion). It's "not doing it right" that counts, which requires not to be vocalised.
To confirm this particular contraction is nonstandard, note just 3 instances of "I mustn't be doing" in Google Books, but 3830 for "I must not be doing" (almost all for the sense relevant here).
I personally find the use of the contraction "mustn't" to be a bit off-putting in this case, but I certainly would have no problem expressing an argument this way:
If John had stolen the money, he would have gotten ink on his fingers when the dye-pack exploded.
John doesn't have ink on his fingers.
Therefore, John must not have stolen the money.
Substituting "can't" for "must not" is valid here, but wouldn't be my natural formulation.
(Generally in this situation, the word not has the same stress as the word must, which is why using a contraction there would sound strange to me.)
The same holds true for situations like this:
"It's supposed to work when I do this!"
"You must not be doing it right".
In that case, saying "You can't be doing it right" would sound very unnatural to me. Or, at the very least, like a Briticism.
I tend to think of "mustn't" as a single lexical unit meaning "must avoid", so if someone said "You mustn't be doing it right", I would first think that they were trying to prevent me from doing it the "right" way.