Let's call that point in the future "tomorrow, 16:00 h".
It will be done at that point in the future.
No-one is doing anything, until tomorrow, 16:00 h. Then what needs to be done, will be done.
It will have been done at point in the future.
At some point in time between now and tomorrow, 16:00 h , what needs to be done will be done. We do not know when exactly it will be done, but will certainly have finished by tomorrow, 16:00 h.
English has no future in the future because English has no future tense at all. English verbs approach tense from two perspectives: before now (past), now and after now (present/nonpast). As such, we can conjugate the verb to eat as follows:
I eat.
I ate.
But there is no way to conjugate the verb for the future, and so we resort to periphrastic constructions to form future aspects, which, for better or for worse, usually infuse other meaning into the sentence:
I will eat (volition).
I shall eat (obligation).
I may eat (possibility/permission).
These all imply future time (and thus form the future aspect), but may infuse undesired meaning into the sentence. Nevertheless, we also have less meaning-rich, albeit more verbose, ways of expressing future time:
I am going to eat.
I am about to eat.
So, although there is no future in the future tense, we can form a future in the future aspect by combining the foregoing constructions:
I will be going to eat.
I will be about to eat.
Both of which sound fine on occasion, but may grate on the ears (eyes) if heard (read) too often, especially in the passive voice: the food will be going to be eaten.
It is also worth noting that the present tense is often used for both present and future time, often making the future aspect seem too verbose where it is still grammatical. Consider the following pairs:
I am going home tomorrow. / I will be going home tomorrow.
He heads out in an hour. / He will head out in an hour.
In each pair, both sentences mean about the same thing and, at least where I live, the average Joe is more likely to say the first. This is merely something to consider, however, and it is not meant to discourage your idea at all.
Best Answer
In fact, both are grammatically correct. But "by noon" is the most common phrase for the English speakers. Literature too abounds of the examples where eminent authors have used "by noon" (All right, sweetheart, I'll be through by noon for sure-The Monster Men by Edgar Rice Burroughs).
Though 'before noon' is correct, but since it is not generally used, nowadays it may seem obsolete and somewhat peculiar to the ears of an English speaker.
Your teacher has corrected your rightly because correct English is the one which appeals correctly to the ears of English speakers. Moreover, even for non-native speakers like me, "by noon" conveys the meaning of "till noon" better than "before noon."