Atticus Finch proves that Tom could not have beaten Mayella Ewell because her attacker had to be left handed. Tom Robinson's left hand was injured years ago and he can't use it. Tom could not have beaten Mayella. She was bruised in such a way that it would have been done so by a left handed attacker.
Atticus Finch proves this but still the jury finds Tom Robinson guilty because he is black. Also, they are not going to condemn Mayella's father over a black man, even though Bob Ewell is a lesser class white citizen. Times were so racially prejudiced until Tom Robinson did not stand a chance for a fair trial. Even Atticus knew this as he suggests when he tells Scout they are not going to win the trial.
'Atticus, are we going to win it?'
'Then why -'
Simply because we were licked a hundred years before we started is no reason for us not to try to win.'
Atticus gives the trial everything he has, but it is not enough. Tom Robinson is convicted of a crime he didn't do:
In Chapter 21 the fulfillment of the mockingbird theme comes to pass. Tom is convicted—but because of his color and not of his guilt. Atticus, who has struggled hard to help Tom, loses the case.