Why do Muslims not eat during the day during Ramadan?

This is among what is required in fasting, it's an order per religion.

Fasting teaches you patience, makes you feel with the hungry poor people, allows you to show you Lord Allah your obedience to Him.

Fasting is a way of gaining Allah's pleasure with you.

The Almighty Allah promised to reward those who fast a special reward.

Fasting Ramadan is one of the pillars of Islam.

Fasting is good for your health & this is scientifically proven.