The short answer
Because he wanted to control what he left behind, and had decided so long before. In July 1790, days before he died, he had two friends burn his unpublished manuscripts.
Two burnings, often confused
The first was only ordered. In April 1773, before leaving for London with the manuscript of The Wealth of Nations, he wrote to David Hume, as his literary executor, to destroy about eighteen thin paper folio books if he died.
The second happened. In the second week of July 1790 he sent for the chemist Joseph Black and the geologist James Hutton, who had been putting him off for months, and would not be put off again. The usual figure of sixteen volumes is a round number reported at second hand. Afterwards, it was said, his mind seemed greatly relieved.
What was lost
Almost certainly the third book. In 1759 he had promised readers an account of the general principles of law and government, and he was still promising it in 1790. The two sets of student notes from his Glasgow lectures on jurisprudence, one published only in 1896, are the shadow it left.
The other fire
It was not the first time he burned things to make a point. A week after becoming a Commissioner of Customs in 1778, he found that nearly all his cravats, ruffles and handkerchiefs were prohibited goods, and burnt them all.
His first biographer drew the obvious conclusion about the papers: he seems to have wished that no materials should remain for his biographers. Most of what is known about him comes from letters that survived because they were in other people's houses.