Spitz and Buck fight in chapter 3, when spitz and Buck were about to fight, a group of dogs trying to steal food from the team interrupted them. and Francois was worried that the huskies could have given their dogs rabies.
Buck killed Spitz because Buck and others did not like the way Spitz treated all of them, Spitz was mean, he laughed about Curly's death, as well he Stole Buck's hiding hole.
Francois treated buck very well, he even ends up rubbing Buck's feet for half an hour each night after supper to help Buck's pain.