Did Jesus speak Aramaic or Hebrew as his language of teaching and interacting with other Jews?

In Part 2 of this interview, (see part 1 here), author Doug Hamp finishes making a compelling case from the Bible that Jesus taught and spoke Hebrew. Doug and Bob then turn their attention to the question of motivation.

Why have so many researchers been so quick to dismiss Hebrew and insist on Aramaic? What is REALLY going on here?