What does the man in the red sweater teach Buck about happiness in The Call of the Wild?

The man in the red sweater teaches Buck that if he wants something, he has to be stronger than everyone else. 

The man in the red sweater teaches Buck the Law of Club and Fang, which means that someone bigger than you will beat you and there is nothing you can do but take it.  You have to be quicker, stronger, faster, and tougher to get what you want.  To be happy in the wild, you have to learn to take what you want or at least not get caught if you are weaker. 

He did not steal for joy of it, but because of the clamor of his stomach. He did not rob openly, but stole secretly and cunningly, out of respect for club and fang. In short, the things he did were done because it was easier to do them than not to do them. (Ch. 2) 

It is not so much about happiness as it is about survival.  Buck might have been happy on Judge Miller’s place, before the days of the man in the red sweater.  In those days, everything was given to him.  He didn’t need to take anything.  There was no Law of Club and Fang.  If you want something in the wild, you have to take it.  You have to be bigger and stronger than everyone else. 

A good example of this is when Buck wanted to be lead sled dog.  Spitz was the lead dog, and he was an enemy to Buck.  Buck had learned the Law of Club and Fang.  To be happy, he had to be lead dog.  He decided to take the position regardless of what the men had to say about it.  He defeated Spitz, and then took his spot. 

Buck trotted up to the place Spitz would have occupied as leader; but Francois, not noticing him, brought Sol-leks to the coveted position. In his judgment, Sol-leks was the best lead-dog left. Buck sprang upon Sol-leks in a fury, driving him back and standing in his place. (Ch. 4)

Nature is harsh.  Buck is a tough dog.  Although his early years were soft, he learned quickly.  If he had not learned his lesson so well from the man in the red sweater, he may not have survived on the sled teams, with the other dogs or in the tough conditions.  Buck was a fast learner, and he found his own way to be happy.