Law /
Poland student visa refusal - 'intention to leave' [51]
Even if there are no "red flags" the consul has the power to reject an application because he/she simply isn't satisfied with something
Exactly. There is considerable, almost absolute, discretion afforded to the consul in such cases, and it is very rare indeed that another consul or superior is going to second-guess his judgement. The burden is 100% on the applicant to prove that they fulfill the requirements of the visa in question, and to eliminate all doubts from the mind of the consul, who not only has the right, but the duty, as well, to be vigilant, cautious and skeptical. The applicant not only has to prove that there are no plausible reasons against granting the visa (or "red flags"), but also that there are abundant and sound reasons for granting the visa.
In this case, the applicant clearly failed to provide sufficient reasons for, and probably provided sufficient reasons against granting the visa, which automatically substantially increases the burden were an appeal to be filed. To the point where there is little hope that a mere prospective student would be able to meet that burden. If he were an established businessman with strong ties to his home country and had the documentation to back it up, an appeal would make sense. But not in this particular case, in which the consul is starting on the firm and well-justified assumption that the applicant is most likely not going to honor the terms of the visa. An appeal would be simply a waste of time and money for all involved. Nor would the nature and status of his application and acceptance into a Polish university be likely to alter anything, as the reason the consul rejected the visa in the first place almost certainly had little, if anything, to do with the decision, which is almost certainly because of the fact that he did not answer the consul's questions in a manner consistent with that of a serious prospective student.
Gosc is also correct that the OP is almost certainly overstating his case and leaving out important details. However, even if more honest details were provided, it would not change the fact that the OP is just not going to be granted a visa to Poland.
One thing you are both missing is that the consul is under no obligation to provide a full or "honest" reason for rejecting the application. They are under no obligation to provide any reason at all. The OP's mistake was to assume that, just because box on the form next to "your intention to leave the territory of the republic of Poland before the expiry of the visa could not be ascertained" was checked, and no others, that this was the only reason that the application was declined. That is hardly likely.