Why did Joseph Smith and Oliver Cowdery confer the Aaronic Priesthood on each other after being ordained by John the Baptist in 1829?

You raise an interesting question. The event you describe is detailed in JS-H 1:71, but other than the statement that they were commanded to do it that way, no further explanation is given, and Joseph never offered any definitive commentary on this point.

My own view is that it was done a second time because the second ordination followed baptism, which would be the normal order of things.  This seems to have been President Hinckley's view as well.  As he stated in the May 1989 issue of Tambuli:

"Those second ordinations, I suppose, were not necessary, but were done to emphasize a lesson. They already had received the authority from John. But they were taught that the receiving of the priesthood was to follow baptism and a pattern for conferring it was established."


For some further speculation on this point on Mormon blogs, see the following:

www.timesandseasons.org

www.mormonmentality.org