Why were Joseph's brothers jealous of his coat of many colors?
Joseph's brothers were jealous because the coat of many colors was a special garment that marked its wearer as the designated head of the brethren. By giving it to Joseph, their father was showing that Joseph, though not the eldest, was being placed over them.
Les explains that in the Middle East, even in antiquity, the eldest son was given clothing that designated his position, and that custom continued. Jacob did this for Joseph with what was probably a coat of many colors. The brothers became jealous because they saw their father designating Joseph as the head of the brethren even though Joseph was not the eldest. Les also parallels this with Rebekah putting Esau's specially designated cloak on Jacob, showing that such clothing marked the eldest's role, though God was sovereignly bringing about His mandate.