I'm 3 days below the requirement. I wrote back the letter to the officer today acknowledging that I did a mistake in counting; I counted my physical presence from the date I was granted my Student visa and not from the first day I entered Canada
I mostly agree with @zardoz. If the facts are clear, that is if it is clear that you are, at best, SHORT three days credit toward the Physical Presence requirement, there is no doubt about the outcome: this application will NOT, CANNOT, lead to a grant of citizenship. Whether you withdraw this application, or it is denied, you will need to make a NEW application in order to obtain citizenship.I redid the calculator and I apologized and acknowledged my mistake and I wrote that I hope the judge will still accept my application and send it back to the officer yesterday.
For emphasis: as I previously noted, IRCC has NO discretion if the applicant is short. There is NO authority to grant citizenship to an applicant who was even one day short AS OF THE DAY THE APPLICATION WAS MADE. (There was back when it was a Residency requirement rather than a Physical Presence requirement, for applications made prior to June 11, 2015, but that is no longer anywhere near relevant.)
Thus, if in the meantime you have been IN Canada sufficiently to now meet the Physical Presence requirement AND you meet all other requirements of course, to obtain Canadian citizenship you can make a NEW application. That appears to be your only path to citizenship.
No need to withdraw the first application before making a new application BUT it is probably best to withdraw the current application sooner rather than later (submitting both around same time is probably OK).
Yes, it is true that this is a factor significantly increasing the RISK of RQ-related non-routine processing for the second application. But you have already crossed that bridge. This RISK factor is triggered as much by the denial of an application as it is withdrawing. And this is not necessarily a big risk and not nearly so negative as one might apprehend even if the new application encounters some RQ-related processing . . . how it will go will DEPEND a lot on whether IRCC processing agents perceive reason to doubt your information. Many who withdrew and reapplied in the past have reported very smooth sailing the next time; they had made easily understood mistakes the first time and were clearly qualified by the time they reapplied.
HOWEVER, I am NOT advising you do this or that. I am NO expert. I am NOT qualified to offer personal advice. I do not know all the relevant facts and thus, even if I was an expert, I could NOT reliably offer any personal advice anyway. (And this is NOT an appropriate venue for attempting to discuss or share anywhere near sufficient details for anyone here to offer personal advice, notwithstanding how much advice is offered in this forum.)
AND this might be an important distinction for you in particular. It appears you have made not just any mistake, but a mistake based on a rather important misunderstanding . . . and frankly, it appears likely there was some misunderstanding during the interview.
To what end I cannot guess. If I was to GUESS I'd guess you have recognized and acknowledged your mistake, and assuming you now qualify for citizenship a new application should proceed fairly smoothly.
That said, that is a GUESS and it is not easy to discern how IRCC sees the situation. Again, it appears there was also some sort of misunderstanding during the interview. Additionally, I am not sure of the procedure once you have acknowledged the error AND that you are short of the minimum actual physical presence requirement. Whether you withdraw (or, perhaps more to the point, ASK to withdraw) or you allow the process to proceed.
I am hesitant to elaborate beyond this. I realize that some of my what-if analyses tend to be, as some put it, "SCARY." I do not want to scare you. I doubt there is much reason to worry. While I emphasize it is merely a GUESS that now things should go relatively smoothly if you make a new application, my impression leans far more heavily that way and hardly at all toward some . . . well, potentially scary what-if alternatives.
So for now I will skip the more scary what-if possibilities. They seem unlikely, unlikely enough to not worry about them . . . and, anyway, you have done what would need to be done anyway, by acknowledging the mistake.
In this regard it warrants noting and emphasizing that you sending communication to IRCC ACKNOWLEDGING and explaining the error, the mistake, should resolve things about as favourably as they can be. This will not change the outcome, regarding qualification for citizenship, since the mistake renders you not qualified for purposes of that application. But other than that, for example, that should preclude or at least greatly mitigate any IRCC perception of misrepresentation. As I have previously observed, IRCC recognizes most people make mistakes, and sometimes some rather big mistakes. IRCC does not go out of its way to punish clients for mistakes. Odds seem good all should go well now if you withdraw and reapply.