Why do some countries declare the legal sighting of the crescent moon despite the moon not conjuncting with the sun, or the crescent moon being below the horizon at sunset?

Imam Al-Subki distinguishes between two scenarios concerning the sighting of the crescent moon when contradicted by astronomical calculations:

1. If calculations indicate the possibility of sighting, but the crescent moon is not seen: In Islamic law, a month is the period between two crescent moons, which is determined either by sighting or by completing thirty days. If the sun's rays depart after dawn, fasting on that day is not obligatory; fasting should begin on the following day. Scholars differed on the ruling of fasting if calculations indicate the possibility of sighting at sunset.

2. If calculations definitively indicate the impossibility of sighting (the crescent moon is very close to the sun): In this case, a visual sighting cannot be presumed. If individuals report seeing it, their report is not accepted due to the possibility of falsehood or error. Even if two witnesses testify, their testimony is not accepted because astronomical calculation is definitive, while testimony is presumptive, and presumption does not contradict certainty. A prerequisite for evidence is that what is testified to must be possible sensually, intellectually, and legally. If calculations definitively indicate impossibility, then acceptance is legally precluded. There is no legal text that obligates accepting the testimony of any two witnesses, regardless of whether what is testified to is true or false. The ruler must not accept such testimony if calculations definitively indicate the impossibility of sighting, and the principle of the month's continuation should be maintained.