In some way you answered the question yourself. Spitz was a bully. He bullied Buck because that was his nature. Spitz was the lead dog. It was his job to lead the team. Buck was a newcomer to the team and Spitz tried to treat him as he had treated all the other dogs. Just like the bully at school, he tried to push Buck around, take his food, and show him who was boss. Buck wasn't going to have it. He was not going to be bullied so he finally fought back and replaced Spitz. The difference was that Buck led by example and earned the respect of the team. Spitz did not earn their respect, he just intimidated them into compliance.
"Spitz is the lead-dog of the team, and he is Buck's nemesis. Buck resents his power and intends to challenge him, knowing that it must be a battle to the death. When Buck, in the full frenzy and "ecstasy" of the "blood lust," closes in on a rabbit, and Spitz steps in to claim the prey for his own, Buck attacks Spitz. After a long and bloody fight, Buck is the victor, the "dominant primordial beast."
becausee, Spitz was intimidated by Buck.