The Splitting of the Moon happened neither of its own accord in consequence of certain causes, nor as a result of chance, nor was it a natural event that occurred through the ordinary laws of nature. Rather, the All-Wise Creator of the Sun and the Moon caused it to happen as something out of the ordinary in order to confirm His Messenger's messengership and to illuminate his claim.
As the mystery of guidance, the mystery of human accountability, and the wisdom of messengership required, it was demonstrated as a convincing proof to certain people specified by dominical wisdom. The mystery of wisdom required that it was not shown to people in every region of the world, who had not yet heard of Muhammad's (PBUH) claim to prophet-hood. Numerous obstacles prevented them, therefore, such as mist, cloud, and time-differences, and the fact that in some countries the moon had not risen, and in others the sun had risen, while in others it was morning, and in yet others the sun had just set.
If it had been shown to all and sundry, it would have been shown as a result of the Sign of Muhammad (PBUH), and a miracle of prophethood, in which case his messengership would have been so manifest that everyone would have been compelled to affirm it. No choice would have remained for the reason. And belief is attained through man's power of choice and his reason. The mystery of human accountability would have gone for nothing. And if it had been shown merely as an occurrence in the heavens, its connection with Muhammad's (PBUH) messengership would have been severed, and it would have retained no peculiarity to him.