Why would John the Baptist give the Aaronic Priesthood to Joseph Smith?
You are mistaken. John did not speak out against the Aaronic Priesthood, but to those who misused it. The Aaronic Priesthood is the right of the sons of Levi (or in other words, the descendants of Levi); which John the Baptist was. As a descendent of Levi, John held the Aaronic Priesthood. See Hebrews chapter 7 for this explanation. The Aaronic Priesthood is the preparatory priesthood, and is the authority to act in the name of God to perform many ordinances, such as baptism. John’s mission was to prepare the way of Christ coming, and he proclaimed such in the Bible. John told the Pharisees that he had the power of God to baptize by water, but that he did not have the full authority that Christ did, as he was “unworthy to unlatch the shoes” of Christ, spoken figuratively. Johns mission to prepare the way of Christ was foretold by the prophets, namely Isaiah who said, “ΒΆ The voice of him that crieth in the wilderness, Prepare ye the way of the Lord, make straight in the desert a highway