It’s aligned with his strategy
Some people theorize that Eminem rarely smiles because he wants to reaffirm the messages present in his songs. Many of Eminem songs are angry songs, and thus smiling more often might make him seem like saying things he doesn’t mean.
He wants to project a certain image
Some people assume that by not smiling often, Eminem can project the image of toughness he wants to project.
He is tough
Some people say that Eminem is tough that he doesn’t like to smile often.
Because he has been through a lot
Some people claim that Eminem doesn’t smile a lot because he has been through too much in his life. Those people cite some of Eminem lyrics as proof to their claims. (See Why some people never smile?)
He believes he looks better this way
Some people claim that Eminem believes that he looks better this way, and that’s why he doesn’t smile much.
It’s aligned with his personality
Some people claim that Eminem doesn’t smile much because it’s a part of his personality. Eminem is a rebel, competitive and sometimes angry person. Smiling a lot might not fit with that personality cluster. (See Why do some people like Eminem so much?)
He actually smiles, but people focus on other pictures
Some people assume that Eminem smiles normally, but people focus on the pictures where he doesn’t go because of his angry songs.
He believes it makes him weak
Some people claim that Eminem might not want to appear smiling because he believes it makes him weak.
No evidence to back any of the those claims
All of those are theories people made with no real evidence to support any of them. They are best effort guesses.