Smitty is a character who is only mentioned once in John Steinbeck's novel Of Mice and Men.
The fight between Smitty and Crooks happened the Christmas prior to George and Lennie coming to the ranch. The boss had brought the ranchers/workers a gallon of whiskey and told them to have fun because Christmas only comes once a year.
Given that the ranchers had the okay of the boss, they decided to drink to excess. Given the men's intoxication, one man, Smitty, was upset at the fact that Crooks was able to join in with the Christmas festivities. Given that Crooks was black, and some of the men were prejudice (notably Smitty), Crooks was challenged to a fight.
Because Crooks was injured and the men did not think the fight would be fair, they made Smitty fight without his feet so as to balance out the fight. Crooks won the fight. Smitty was angry saying that the only reason that Crooks was able to beat him was because of his inability to use his feet. Smitty was so sure of this he even stated that he would have killed Crooks.
Therefore, the whole reason that Crooks and Smitty fought was because of the drunkenness and the racist attitude of Smitty.