Why do Muslim women wear the Abaya?
First and foremost, the main reason why Muslim women cover up is because they believe it is the commandment of Allah. For example, in the Quran, it says, "Say to the believing men that they should lower their gaze and guard their modesty; that will make for greater purity for them; and Allah is well acquainted with all that they do."
"And say to the believing women that they should lower their gaze and guard their modesty; and that they should not display their beauty and ornaments except what must ordinarily appear thereof; that they should draw their veils over their chests and not display their beauty except to their husbands, their fathers..." It might leave room for other interpretations. But by and large, most Muslim women believe that they should wear the Abaya.