what have i done that you should be so angry with me?请问这句话中,

should 情态动词 通常用于许多表示情感的形容词后的that从句中,表示“竟然”的意思.
例句：I found it astonishing that he should be so rude to you.他竟然对你这样无礼,真让我吃惊.
What have I done that you should be so angry with me?我做了什么,你竟然会这样对我生气?
这是个what引导的特殊疑问句,语序倒装,所以用have I done,而后面的that又引导了一个定语从句,用陈述语序.should在定语从句中是情态动词,加强语气,表“竟然”.