In college and high school, I believe that I could have benefited to some extent from having been tipped off at some point to constantly and seriously question my own larger purpose in attending college, and whether the foundations I was setting then, beyond increasing my own basic knowledge and experience, were sufficiently solid to support that purpose without significant and possibly costly external intervention. At some level it should be perfectly fine to pursue one's work in private and to allow the larger questions of how one's own integrity coheres within a larger sort of 'integrity matrix' to resolve themselves subconsciously. But at another level, the less one is able to accomplish oneself, the more one must perhaps subconsciously rely on labor done by others who may not ultimately benefit from one's gratitude. Hence, I can imagine there being considerable value in inviting students to take these kinds of meta-matters into their own hands, and deliberately build and test their own academic infrastructure to whatever extent they are able.
The modern Academic Integrity movement in the U.S. can be attributed to Donald McCabe, although it has existed in various forms for much longer.
By now there is a wealth of additional perspectives on this topic, with more or less complexity or explanatory power.
As is often the case, academic integrity has been enforced for longer than conscious attempts have been made to understand it, and has been upheld through a variety of accounting mechanisms, and this context shapes or limits how the field itself can be studied and understood going forward.
The movement appears to be rooted in the subjective experience of what is regarded as fair or just at an individual level, as well as the objective experience of what may be universally regarded as true in a society. There can be more or less tension between these constitutive elements, especially where several different societies begin to overlap or rub against each other.
Within many societies (including most U.S. academic settings to my knowledge) authorship is regarded as an extremely personal quality, and is tied to the status (or grant funding, or influence) of an individual within that group.
In others, the role of an individual in achieving a certain desired result is viewed as secondary to the success of a group as a whole: a person's contributions are noted only to the extent that doing so increases the chances of the group succeeding in its future tasks, and are otherwise thought of as being in vain, or purely egocentric.
It might be interesting to examine what might happen at the junction of these very different philosophies toward scholarship, if doing so is not perilous. One might hope that the collective goals of academia are to bring a sensitive lens to bear on poorly understood subjects, and not an opposite thereof.
Note that a strict individualistic approach to academic integrity is not necessarily individualistic in its impact or intrinsically egocentric: it could serve the needs of the society in which it is maintained as well as an explicitly collectivist approach would, for example by deliberately attracting talented researchers from elsewhere. There would also be strong incentives to monitor individual behavior, and for individuals to express their values as faithfully as possible.
If the individualistic approach is clumsily or selfishly implemented, however, it could easily turn into a counterproductive and/or corrupt sort of self-ingratiation.
Objective stances toward academic integrity are most prominent in exam rooms and, to some extent, the evaluation of long-form essays. Short assignments tend to be given slightly less official scrutiny, for better or for worse, though often owing to technological or time constraints rather than limits to the inherent meaning of the work.
In the literature (c.f.  and ) there appears to be a tendency for academic integrity to be defined in terms of one of its opposites: cheating. This is a potentially untenable habit, as the notion of cheating is itself somewhat treacherous; its meaning is unambiguous in certain cases, but less so in others, and sometimes in counterintuitive ways. Can two students be accused of cheating if their answers on a test are conspicuously similar, if the teaching staff failed to notice it during the exam? Some might say yes, but would it not be cheating to allow cheating to occur, or to presume guilt, or punish without a hard justification? Moreover, there are other behaviors that can be corrosive to (certain interpretations of) academic integrity when taken to extremes, behaviors that are not obviously cheating: student isolationism or self-imposed hermitude (which can seem, subjectively speaking, like the complete opposite of cheating), enrolling in subjects that one has already studied elsewhere, or accidentally leaving one's bag unattended in a restaurant for 15 minutes. A philosophy of academic integrity expressed only in terms of cheating might be somewhat akin to a philosophy of virtue that is grounded entirely in (technical) prowess.
Be that as it may, how one might approach the subject of academic integrity in a constructive or positive way is a very sensitive matter, in part because of the ethical quandaries that surround the murky business of telling other people how to hold themselves accountable, or what kinds of pledges or promises or vows to make, or perhaps even suggesting that it is even possible to make pledges or vows in ways that are both meaningful and safe, as though doing so did not also involve accepting certain risks as well. It is somewhat nontrivial to come up with an explicit personal accountability framework that is both sound and allows one to make what amount to real, considerate, and unassailable, promises to others, but that (and, in an a posteriori sense, accommodating or forgiving impudence, possibly the 'grit' alluded to in Buffy's answer above) is essentially what academic integrity requires.
 Pedagogy not Policing: Positive Approaches to Academic Integrity at the University, https://press.syr.edu/supressbooks/2413/pedagogy-not-policing/
 Cheating in College: Why Students Do It and What Educators Can Do about It, https://jhupbooks.press.jhu.edu/title/cheating-college