The only people who date Daniel that late are those who deny that prophecy exists. Daniel was so accurate about the future that liberal theologians (who deny the supernatural) and their students late-date Daniel to make it appear he is reciting history instead of prophesying the future. In fact, the anti-supernaturalists don't even believe Daniel wrote the book named after him.
Alexander the Great and Daniel
JOSEPHUS [Antiquities, 11.8.5] mentions that Alexander the Great had designed to punish the Jews for their fidelity to Darius, but that Jaddua (332 B.C.), the high priest, met him at the head of a procession and averted his wrath by showing him Daniel's prophecy that a Grecian monarch should overthrow Persia. Certain it is, Alexander favored the Jews, and JOSEPHUS' statement gives an explanation of the fact; at least it shows that the Jews in JOSEPHUS' days believed that Daniel was extant in Alexander's days, long before the Maccabees, and long before 167 BC.
What you have to believe if Daniel didn't write the Book of Daniel
The (critics of Daniel) cannot believe in miracles and predictive prophecy which involve nothing but a simple faith in a wise and mighty and merciful God intervening in behalf of his people for his own glory and their salvation; BUT THEY CAN BELIEVE that a lot of obstreperous and cantankerous Jews who through all their history from Jacob and Esau down to the present time have disagreed and quarreled about almost everything, or nothing, could have accepted, unanimously and without a murmur, in an age when they were enlightened by the brilliant light of Platos philosophy, and Aristotles logic, and the criticism of the schools of Alexandria, a forged and fictitious document, untrue to the well remembered facts of their own experience and to the easily ascertained facts concerning their own past history and the history of the Babylonians, Medes, Persians, and Greeks of whom the author (of the book of Daniel) writes. R.D. Wilson, Studies in the Book of Daniel, pages 268, 269
The Sanhedrin of the second century B.C. was composed of men of the type of John Hyrcanus; men famed for their piety and learning; men who were heirs of all the proud traditions of the Jewish faith, and themselves the sons of successors of the heroes of the noble Maccabean revolt. And yet we are asked to believe (by the critics of Daniel) that these men, with their extremely strict views of inspiration and their intense reverence for their sacred writings, used their authority to smuggle into the Jewish Canon a book which, ex hypothesi, was a forgery, a literary fraud, and a religious novel of recent date. R. Anderson, Daniel in the Critics Den, pages 104-105