Why is it required to perform ablution after passing gas?

The emission of wind (flatulence) invalidates ablution (wudu') by scholarly consensus, and they have cited Prophetic hadiths such as: "The prayer of one who has passed wind is not accepted until he performs ablution," and his (peace be upon him) saying to one who imagines finding something during prayer: "He should not leave until he hears a sound or perceives an odor."

Ibn al-Qayyim pointed out that distinguishing between wind emitted from the anus and belching is one of the beauties of Islamic law; the former exits from the place where feces emerge and may be accompanied by moisture, whereas belching is wind that is trapped above the stomach.

Islam teaches us that what Allah has legislated is the essence of wisdom, and a true Muslim adheres to the commands of Allah and His Messenger (peace be upon him), whether he comprehends the wisdom behind them or not. If he does comprehend it, that only increases his submission.