Chamberlain is not "regular army," but a former college professor. He is used to dealing with irritable, unruly students who question things, and he is used to discussing things to bring about an agreement, rather than threatening to "shoot" someone into compliance. His "professor's mind" questions things instead of accepting military dogma. He thinks deeply on the meaning of life and man, and he has a basic humanitarian and fatherly approach to dealing with his men. He cares for their needs and then leads them.
His basic humanity toward others is what ultimately reaches the mutineers and convinces them to join the 20th Maine. They have been fed, heard, spoken to kindly, respected for what they've already done in the war, and they are not going to be shot if they don't fight. They are willing to take a chance following Chamberlain.
Also, Chamberlain is a Maine man. The importance of allegiance to your home state first above everything is shown in the interchanges about "Maine men." You see the interstate rivalry and inter-unit disdain when the Pennsylvania captain who delivers the mutineers treats all Maine men with disgust.
The importance of Chamberlain's convincing the mutineers to join his regiment will be seen later as the battle at Gettysburg unfolds.
