Why does islam encourage covering female bodies?

According to Wikipedia : > Koran says: Say to the believing men that they cast down their looks and guard their private parts; that is purer for them; surely Allah is Aware of what they do. And say to the believing women that they should lower their gaze and guard their private parts; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their khimār over their breasts and not display their beauty except to their husband, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. — Quran 24:30 There are also some hadith supplied. However, nowhere does it explain **WHY**. Why does Islam encourage covering female bodies? 1. Is it because to keep society civil? 2. Is it to protect women from sexual harm? 3. Is it because to preserve modesty? 4. anything else? Please, answer with appropriate authentic references.