To understand the Documentary Hypothesis, we need to begin by considering this question: why do people think Moses authored the Pentateuch? The main reason derives from Deuteronomy 31:24–26: “When Moses had finished writing the words of this Law (tôrāh) in a book to the very end [that is, the Book of Deuteronomy], Moses commanded the Levites who carried the ark of the covenant of YHWH, ‘Take this Scroll of the Law (sefer ha-tôrāh) and put it by the side of the ark of the covenant of YHWH your God, that it may be there for a witness against you.’” (ESV, modified) Technically this passage refers only to the book of Deuteronomy, but it has generally been interpreted by traditional exegetes to refer to the entire Pentateuch. (See also Exodus 24:4; Numbers 33:2; Deuteronomy 31:9.)
Outside of the Pentateuch itself, many authors of the Old Testament/Hebrew Bible seem to have believed that Moses wrote the Law. Joshua 8:31 refers to Joshua copying “the Law of Moses, which he [Moses] had written.” Mosaic authorship of the Pentateuch is likewise implied in many other passages (2 Kings 21:8; 2 Chronicles 33:8, 34:14; Ezra 3:2; Nehemiah 8:1, 9:14, etc.). If, as many scholars assume, the “Scroll of the Law” (sefer ha-tôrāh) discovered in the temple as described in 2 Kings 22:8 is an early form of the book of Deuteronomy, then by the late seventh century BC at least, many Israelites believed that Moses had written the Scroll of the Law.
The Documentary Hypothesis thus directly challenges this ancient claim of Mosaic authorship of the Pentateuch, which was assumed by nearly all biblical authors. Hence, the controversy begins.