At UCLA, Bauer, the eccentric mad scientist "nerd", won a bunch of national college baseball awards in 2011 and had an outstanding season.
Cole, the "jock", had a great season the year before, but his performance declined a little bit in 2011 — right when Bauer got a lot of national attention. There's probably a little jealousy factor from that year.
Bauer, in addition to his unorthodox approaches to pitching, has a brash and sometimes abrasive personality. He chalks some of this up to being bullied in high school, and even at UCLA — you can make a pretty good guess by who. His personality is also what got him traded from the Diamondbacks.
One thing I find particularly weird is Cole supposedly saying to Bauer that Bauer had no work ethic. Bauer really doesn't have a typical pitcher physique, but has obsessively trained himself to get to where he is today. Cole is much more naturally gifted. I could see Bauer holding a grudge towards Cole over comments like that.