The man in the red coat or sweater teaches Buck about power. Buck learns that if there is someone or something that is in power above you, he/she/it must be obeyed. The man in the red sweater teaches Buck this lesson with a club after he buys Buck. The man opens the crate, Buck lunges at the man, and the man beats Buck back with a club. Buck lunges again and the same thing happens. Buck tries again and again until he is beaten and bloodied.
In the most simple lesson possible, Buck learns to not attack anybody with a club. But the lesson runs deeper. Buck has learned not to attack anybody that has a weapon. Further still, Buck learn about power. Don't attack someone that has more power than you. In that situation it is better to submit to the authority. Be patient and wait until you are more powerful.
"He had learned the lesson, and in all his afterlife he never forgot it. That club was a revelation. It was his introduction to the reign of primitive law, and he met the introduction halfway. The facts of life took on a fiercer aspect; and while he faced that aspect uncowed, he faced it with all the latent cunning of his nature aroused. As the days went by, other dogs came, in crates and at the ends of ropes, some docilely, and some raging and roaring as he had come; and, one and all, he watched them pass under the dominion of the man in the red sweater. Again and again, as he looked at each brutal performance, the lesson was driven home to Buck: a man with a club was a lawgiver, a master to be obeyed, though not necessarily conciliated."
I don't need the red coat man I need the others