▲你的句了中的 that 从句是主语从句，句首的 it 是形式主语。类似的如：

It’s annoying that we didn’t know about this before. 令人恼火的是，我们事先并不知道这一切。

It’s annoying that we can’t travel until Thursday, but the upside is that the fare’s cheaper then.  烦人的是我们要等到周四才能出发去旅行，但好处是到时票价会便宜些。

▲有时不是从句，而是不定式（也是用作主语，句首的 it 是形式主语）。如：

It’s annoying to have to get authorization for spending such piddling amounts of money. 花这么一点钱也要去请示，真烦人。

It’s annoying to have to explain this a second time. 还要把这事解释一遍，这太让人恼火了。

▲annoying 并不表示“心情”，annoyed 才表示“心情”。如：

I am annoyed that he didn’t tell me. 他没告诉我，我很不高兴。

Sandra was very annoyed that I was late. 我迟到了，桑德拉非常生气。

Mr Davies was annoyed that the books were missing. 戴维斯先生生气了，因为那些书不见了。

The fans were annoyed that the team gave away such a soft goal. 球迷因球队丧失了如此容易的进球机会而大为不满。

这样的 that 从句有人认为是宾语从句，有人认为原因状语从句（个人比较倾向于后者）。