Arameic vs. Hebrew

I saw Mel Gibson's The Passion of the Christ and liked its property of using the languages particular to the time and space.

I wonder why Gibson used Aramaic instead of Ancient Hebrew as a language spoken by the Jews of the time (including Jesus, or Jeshua ben Joseph of Nazareth). Considering the role of language in defining identity, paired with political allegations, one might suspect that this is a device to de-Jewify Christ, in spite of the fact that Christianity continued to survive as a Jewish sect for some time, until St. Paul managed to persuade the elders to let gentiles become Christians (without being circumsized).

Both languages belong to the Semitic family (which also includes Arabic). According to NPR article, a French scholar claims that "Jesus would have spoken the local dialect, referred to by scholars as Palestinian Jewish Aramaic."

Who spoke Hebrew, then?