Later, it was so that the women wouldn't be raped by their coreligionists. As the Cat Meat sheikh in Australia explained, an uncovered woman is just uncovered meat to a Muslim (cat).
Why women must cover themselves (and why non-Muslim women are increasingly being targeted by Muslims for rape and other atrocities):
"And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, 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 . . ." (Qur'an 24:31).
"Aisha used to say: 'When (the Verse): "They should draw their veils over their necks and bosoms," was revealed, (the ladies) cut their waist sheets at the edges and covered their faces with the cut pieces'" (Bukhari Volume 6, Book 60, Number 282).
"Narrated 'Aisha: 'Allah's Apostle used to offer the Fajr prayer and some believing women covered with their veiling sheets used to attend the Fajr prayer with him and then they would return to their homes unrecognized'" (Bukhari Volume 1, Book 8, Number 368).
[Explanatory note: Shaikh Ibn Uthaimin in tafseer of this hadith explains: "This hadith makes it clear that the Islamic dress is concealing of the entire body as explained in this hadith. Only with the complete cover including the face and hands can a woman not be recognized. This was the understanding and practice of the Sahaba and they were the best of group, the noblest in the sight of Allah . . . with the most complete Imaan and noblest of characters. so if the practice of the women of the sahaba was to wear the complete veil then how can we deviate from their path?"]
"Narrated 'Aisha: 'The wives of the Prophet used to go to Al-Manasi, a vast open place (near Baqia at Medina) to answer the call of nature at night. 'Umar used to say to the Prophet "Let your wives be veiled," but Allah's Apostle did not do so. One night Sauda bint Zam'a the wife of the Prophet went out at 'Isha' time and she was a tall lady. 'Umar addressed her and said, "I have recognized you, O Sauda." He said so, as he desired eagerly that the verses of Al-Hijab (the observing of veils by the Muslim women) may be revealed. So Allah revealed the verses of "Al-Hijab" (A complete body cover excluding the eyes)'" (Bukhari Volume 1, Book 4, Number 148).