To be clear, the IRCC web page linked above lists PROHIBITIONS, things which will prohibit the grant of citizenship.
Additionally, obviously, failing to meet any of the necessary qualifications for a grant of citizenship will also result in the application being denied . . . or "rejected" one might say.
The eligibility requirements, ranging from necessary physical presence to language ability, are clearly described in IRCC's instruction guide.
While it should not arise often, it might be worth mentioning that meeting the language requirement (unless exempted) requires BOTH:
-- submitting proof of meeting this requirement WITH the application, as prescribed in the instructions, AND
-- also showing competence in one of the official languages during the interview
Thus, for example, even though the applicant has and submits an acceptable form of proof of language ability with the application, if the applicant is unable to demonstrate language ability during the interview, that is a reason, "grounds," for denying the application. Basically all that is necessary is for the applicant be capable of responding to the questions asked during the interview, without any interpreter, in English or French .
It is also worth emphasizing that the citizenship applicant must be eligible as of the day before applying and CONTINUE to be eligible right up to taking the oath and being delivered the certificate of citizenship. An arrest for an indictable offense (even if later totally dismissed) the night before taking the oath will prohibit taking the oath and result in the application being denied. Which brings up another very important reason a citizenship application can be denied: misrepresentation, including misrepresentation by omission.
And, to be clear, this latter reason not only is one for which the application can be denied, it is a reason for revoking citizenship . . . forever.
Take the applicant married to an unreasonably cantankerous spouse who pushes things the night before the oath leading to a situation in which the police come and, unfortunately, the police believe the spouse not the applicant, and it is the applicant who is charged with a domestic violence offense. The applicant is fully confident this charge will get dismissed. So, show up for the oath and take the oath without saying anything? BAD BAD BAD idea. Especially if the applicant's spouse really is the unreasonable sort. The failure to disclose an arrest is perhaps (now, these days) the MOST LIKELY REASON why IRCC will pursue proceedings to revoke citizenship. And that unreasonable spouse knows all about it. Consider the poison letter, the fraud tip, written and ready to send.
The misrepresentation reason for denying citizenship warrants further emphasis because misrepresentation is grounds to deny the application EVEN IF what is misrepresented does NOT mean the applicant was actually ineligible. ACTUAL EXAMPLE: applicant advised by consultant that Montreal processing times were way, way long, and the consultant suggested using an address in Ontario for a local office known for fast processing times. Application denied, even though the applicant claimed to nonetheless be living in Canada all that time, just not at the Ontario address used in the application. While there are not a lot of reported instances in which those using a friend's or family member's address, rather than where they were actually living (for a variety of reasons, such as moving around a lot due to working at different locations), have had this cause CIC or IRCC to find misrepresentation and deny the application, it warrants a CAUTION, there are RISKS, any untrue information in the application risks the consequences for misrepresentation.
ALL THAT SAID: This is actually a huge topic with scores of tangents. Most should be obvious. Another reason, a rather obvious reason for denying the application, for example, is failing to show up for a scheduled event. Abandonment can also be deemed if an applicant fails to timely respond to requests.
Thus, it does not make much sense to attempt covering all the possible reasons and tangents in a single topic. And, indeed, this forum more appropriately tends to have individual topics addressing particular issues. There are several, for example, in which questions about meeting the actual physical presence requirement are discussed, including the particular procedures in such cases, noting that applicants claiming to have met this requirement cannot be unilaterally denied citizenship by IRCC but must be referred to a Citizenship Judge (in contrast, a Citizenship Officer can and will unilaterally deny a citizenship application if the officer determines there is an applicable prohibition, as just one example).
Many of the reasons are so obvious and simple, they are not discussed much. For those reasons which tend to be a little complicated, see or start another topic.