The reason why I was sad was that he didn't understand me.that前的was是不是错的?那为什么前加was?

对的呀
the reason was that he didnt understand me 原因是因为他不理解我
the reason why i was sad 我很难过的原因
连起来就是: 我很难过的原因就因为他不理解我
the reason why i was sad was that he didnt understand me

不是

错的，应去掉，这是从句。

没错，因为错误已经能够发生

没错,这样看句子:
The reason (why I was sad) was [that he didn't understand me.]

不是
that he didn't understand me.是表语从句,由was 引导的

The reason why I was sad was that he didn't understand me.
这个我通常让学生当句型背的,很正确的
The reason (why+句子)was that+句子
中文就是"什么什么的原因是什么"
因此你给的这句话就翻译成:我伤心的原因是他不理解我.
why引导的是定语从句修饰前面的the reason,整个句子的谓语动词就是that前面的was,所以绝对不能去的.that引导的是表语从句.
写成简单的就是
1.The reason was that he didn't understand me.
2.I was sad for the reason.
for which相当于why
刚刚给你的句型就是上面提供的两个句子的结合.
最后建议你有空多向你的任课老师请教,多了解句式结构,网上的文字毕竟没有老师当面讲来的效果好.

看怎么理解了 如果时间点是个过去的话 语法没有错
参考
我所以伤心是因为他不理解我.