How does Tom Robinson's testimony both help and hurt his case? Why does one thing Tom says, hurt his case? To Kill a Mockingbird by Harper Lee

In addition to what has been stated, when Tom Robinson
takes the stand in Chapter 18 of To Kill a Mockingbird, he has to
guide his useless left arm onto the Bible in order to be sworn in.  However, his hand
slips off and when he tries to put it back, it slips again.  Judge Taylor growls,
"That'll do , Tom."

It becomes obvious, then, that Tom
Robinson could not have struck Mayella, whose injuries are on the right side of her
face, even before Atticus questions him.  As he responds to the questions of Atticus,
Tom is direct and polite.  When Atticus asks him if he has ever entered the Ewell
property without express permission, Tom replies three times without taking a second
breath, "No, suh, Mr. Finch."  Scout observes that he is a "respectable Negro."  And, he
is kind.  But, this kindness is what damages his chances of an acquittal.  For, he says
what is not politically correct for the 1930s:  He says, "I felt right sorry for her,
she seemed to try more'n the rest of 'em."  Expressing pity for Mayella is construed in
a segregated Southern town to mean that Tom puts himself above Mayella.  And, of course,
even though Mayella is "white trash," she is still white and not socially beneath Tom. 
This statement of Tom Robinson's underscores the theme of racial
prejudice.