What lesson does the man in the red sweater teach Buck in Call of the Wild?
The man in the red sweater teaches Buck that he will submit to man.
After two days without food or water, Buck arrives in Seattle, where he is taken off the train. The men who have carried the crate containing Buck put it down and then "a stout man" wearing a red sweater signs the book for the driver. When they see that Buck's eyes are red with rage, the other men ask the man in the red sweater if he is going to let the dog out, and he replies "sure" as he drives a hatchet into the crate to pry it open. The four men instantly climb to safe perches from which they can watch.
As soon as the crate is opened, Buck lunges for the man in the red sweater; however,
[I]n mid air, just as his jaws were about to close on the man, he received a shock that checked his body and brought his teeth together with an agonizing clip.
The man in the red sweater has clubbed Buck to the ground. This is the first time that the dog has been struck. Nevertheless, Buck gets up and lunges a dozen times only to be knocked to the ground in agonizing pain. After a particularly brutal blow, Buck staggers and then he is struck upon his nose. In tremendous pain, Buck tries again. But, he finally crashes to the ground, learning that this man is a superior force.
The man in the read sweater teaches Buck a lesson about power. The man in the red sweater opens Buck's crate, and Buck lunges at the man. The man has a club that he uses to hit Buck with. Enraged, Buck goes after the man again, and again, and again until he is beaten and bloodied.
On a very simple level, Buck learns to not attack anyone with a club. A bit deeper than that is that Buck learns not to attack anyone with a weapon. Deeper still, Buck learns to not attack anyone that is more powerful than Buck is. Buck learns to submit to a more powerful authority.
The lesson also teaches Buck that he can always become more powerful. He has to be patient and learn to become the more powerful individual. Until that happens though, Buck must submit to the higher power and authority.