Now, for our more liberal readers, it most be born in mind that Kitchen is not a backwoods fundamentalist who teaches at Bob Jones University, but rather a well respected Egyptologist who taught for many years at Liverpool University in England. He is one of the foremost experts on the 13th to 12th century BC in Egypt. One of his most respected works is a biography of Rameses the II. So, he's an expert on the ANE, but he is not a biblical scholar.
Why does Kitchen think that Moses/Moses' assistants composed the Pentateuch?
1. The descriptions of life and political conditions of the eastern delta in the 13th century BC (which Exodus portrays with exactitude) would not have been known to a later author.
2. The geographical information about Sinai (quail migration patterns, water that comes out of rocks, the location of different oasis and deserts) would not have been known to a later in Hebrew author in Israel or Babylon.
3. The Middianites ceased to exist (from what we can tell) after the 11th century BC. A later author would not have known about them or made up stories about them.
4. The treaty forms used in the covenant making scenes Exodus narratives were not used later than the 11th century BC. Actually, they were not used before the 14th century BC. For this reason, Kitchen rejects the early Exodus theory (15th century BC). As he noted earlier, the archaeological data suggests an Israelite invasion in the mid-late 13th century BC. This combined with the fact that the treaty/covenantal forms used only existed and were used during this short window, makes it almost certain that the exodus took place in the 13th century BC and that the Pentateuch was composed at that time.
5. Moses as a figure who spent time in the Egyptian court is highly necessary for this to work to exist as it does. First, the fact that he did spend time in the Egyptian court makes perfect sense in this period in that it was well documented that the children of Semites or "Asiatics" were taken into the Egyptian court and adopted. If the Pentateuch displays these treaty forms known the Egyptians via their contact with the Hittites (Deuteronomy follows exactly the format of a Hittite vassal treaty form!), it would take someone educated by the Egyptians to explain how exactly it would make its way into the Hebrew Scriptures. No author existing during the so-called Deuteronomic reforms (Josiah) would have known these forms and therefore it would be absurd to suggest their authorship during this later period. Neither would slaves escaped from Egypt know them, anymore than I know what modern American international treaties look like! Therefore, only a leader who had been trained by the Egyptians during this exact period would have been able to compose the Pentateuch.
6. One objection might be that the Pentateuch is written in standard Hebrew script which did not exist until later. True. Nevertheless, their was a Canaanite alphabet that existed with 24 characters that many different western Semite groups used. In all probability, Moses and his associates wrote down the Pentateuch in this form. Later on, probably at the time of David or Solomon, when the paleo-Hebrew alphabet had come into existence, the Pentateuch was recopied in this script, which new grammatical forms added. Updating on the spellings of certain words also probably took place. This is not merely speculative or special pleading. Kitchen notes that this was a regular practice in the ANE. It is well documented and continuous through the period in many different civilizations. In light of the geographical information, historical conditions and the treaty forms that only a Hebrew (trained by the Egyptians no less!) in the 13th century would know about, claiming that it is a later composition or even non-Mosaic authorship is special pleading.