Why did Buck follow Thornton around everywhere?

Buck follows Thornton around for the simple reason that he's become deeply attached to him. Although Buck is beckoned to the forest by the call of the wild, he always returns to Thornton's fireside whenever he gets the opportunity. He doesn't have to do this; he does it because he wants to. This demonstrates that his bond with Thornton is based upon a deep, abiding affection rather than fear, as if often the case with relationships between man and dog.
At the same time, however, this relationship, though built upon great love and affection, isn't really good for Buck in the long-term. However kind Thornton may be, he's still in a position of dominance over Buck. This stands in contrast with Buck's natural domain in the forest, where he can truly be his own master, and not beholden to anyone.
Though a genuinely good man on the whole, Thornton's only human. And we see him abuse Buck's love and loyalty when he makes a wager that his dog can pull a thousand-pound sled, break it out of its runners, and "walk off." In effect, Thornton is exploiting Buck; risking his health and welfare for the sake of a bet. But Buck goes along with the stunt, not because he's forced to, but because he wants to out of loyalty to his master. Even so, Buck's true nature is being suppressed by his relationship to Thornton, and he needs to hark the call of the wild before it's too late, before he loses his identity completely.