The fight between Buck and Spitz is said to be ‘inevitable’ because Buck wants to challenge Spitz for leadership of the sled team. The narrative explains why:
It was inevitable that the clash for leadership should come. Buck wanted it. He wanted it because it was his nature, because he had been gripped tight by that nameless, incomprehensible pride of the trail and trace—that pride which holds dogs in the toil to the last gasp, which lures them to die joyfully in the harness, and breaks their hearts if they are cut out of the harness. (chapter 3)
Buck, then, takes great pride in his work on the team – the mark of a good and effective sled dog. This makes him ambitious for the leadership. He knows he can achieve the top spot as he is strong enough to fight for it. He is the only dog to seriously rival Spitz as leader as he has greatly progressed in skill, cunning and strength since joining the team.
Therefore, a fight between the two dogs becomes certain. Buck is determined to challenge Spitz and Spitz is equally determined to fight this challenge and maintain his place at the top. When it comes to the crunch, Buck proves himself superior not just in fighting prowess but also mental capacity. He thinks of a way to finally outwit his enemy and it works.
Buck thus proves his credentials as the best dog on the team. His victory over Spitz is the first major step on his way to becoming the most powerful dog of all, as he sheds every last trace of his former domesticated nature to become the wildest of all wild things. By the end of the novel he has, indeed, attained mythic proportions among the local Indians as the fearful Ghost Dog, the undisputed leader of a pack of wolves.