The problem you allude to here is one that has no simple single explanation. In my studies of this issue, I believe there are three main factors which contribute – grip area, borgar construction, and mouth size/bite technique.
First, it is a given that the average Japanese anime girl has smaller hands than the general population, even when looking specifically at Japanese statistics in isolation. The result is not so much a deficiency of absolute clamping strength as it is the inability to cover a sufficient portion of the lateral area of the bun, and the resulting lack of internal friction. This allows for more displacement of the inner layers of the borgar relative to the bun.
Second, in many of the cases shown in this thread, it is clear that there are multiple layers within the borgar stack that are by their nature ‘slippery,’ and that these layers tend to be directly in contact with each other or buffered only by sauces which provide a lubricating effect, rather than being broken up properly with ‘grippier’ ingredients – crisp bacon or lettuce, a center bun section, or some other structurally significant anchor. Coupled with the lack of compressive stress from the first point, this is a recipe for sudden internal movement and failure of the overall structure.
Finally, as with their hands, the average anime girl mouth is small, the bite depth is minimal (concentrating itself along the edge of the borgar, where edges of layers may not align vertically), and the both the angle of the bite and the inclination of the borgar at the time of biting tend to incline the borgar down from the mouth. This all contributes to a tendency for any slippage to occur out the side of the borgar farthest from the bite, resulting in the catastrophic failure shown in these images.
In my professional opinion as an American Borger Chef (ABC), I believe there have been enough images taken of the moment of failure to say that each of the factors above are common to the overwhelming majority of these incidents. It is possible there are other causes not shown – intelligence may be an underlying component in some or all of these factors, but trying to assess that strictly from the images is difficult at best. Perhaps more research is needed into this specific question.