I always advise my kids to staple on a 45 degree diagonal. This results in the least stress and thus minimizes the chances of the paper ripping.
I had a professor who deducted points for horizontal/vertical stapling. Since some kids didn't follow his reasoning, he spent an entire lecture proving his point. Since then, I have always stapled at an angle.
Some people, however, prefer the vertical or horizontal affixation for purely aesthetic reasons or to make sure that the reader's attention is purely on the text of the document.
They may not like the jarring visual discontinuity that results from the crisp white (or slightly off-white) right angle of the corner of the paper is juxtaposed against a free floating staple that forms a somewhat incomplete triangle.
Instead of their eyes being drawn either to the right, in the case of a horizontal staple, or downward, in the case of a vertical staple, the author of the document may be terrified that the reader of the document may find their eyes drawn to the subtle optical illusion of the triangle.
In addition, when such documents are reviewed, instead of the reader turning the page, in the case of a vertical staple, or flipping the page upward, in the case of a horizontal stable, the pages joined by a diagonal staple awkwardly pulls the readers attention to the off-angle.
If the document is provided to a member of the judiciary who is troubled by such a disruption in their normal way or reviewing documents, or counter to the express rules of document preparation, they may find that their entire argument is rejected due to the stress of the (ostensibly insignificant) violation of the rules.
