Allah says in the quran: . So turn your face toward al-Masjid al-Haram. And wherever you [believers] are, turn your faces toward it [in prayer]. (2:144)
Thus, we need to face the kaaba.
Since our world is a globe, technically speaking, we can face 2 directions, one closer one further. However, you would have to face the closer direction, because facing the more distant direction would be considered having your back to the kaaba.
Imagine you are in Makkah near the Kaaba. You would be expected to face it, and if you turned around and faced the other way, you would not be considered to face the kaaba.
Also, when the Prophet (Saw) migrated to Madinah, he was faced with the dilemma of whether to face masjid ul aqsa, the qibla of many prophets, or the Kaaba, the qibla of Ibrahim (as). In Makkah, he used to pray in such a direction that both were faced. In madinah, this wasnt possible as Makkah was to the south and and masjidul aqsa to the north. Thus, he faced masjidul aqsa until commanded to face kaaba.
if both directions were permitted, this would not have been an issue. since it was, that means that the shortest distance must be faced.