How is Tom wrongly punished for something Sid did? Why doesn’t Aunt Polly admit her mistake?

Tom is beaten when Sid steals sugar and knocks the sugar bowl off the table. Aunt Polly had just reprimanded Tom for trying to steal some sugar himself..... thus, Aunt Polly wrongly blames him for the broken bowl. Aunt Polly doesn't admit her mistake because she doesn't want Tom to think she's soft..... and because she knows he will try it again the first chance he gets.