About Why?

when i  ask why the sentence use rather..than..  I can't explain  exactly.  

Mexico’s President Canceled His Meeting With Trump Rather Than Pay For The Wall

一.why 能引导下列几种从句

1.主语从句     Why he took Chinese nationality  in 1901 is a question that interests us.

Why he love the girl deeply?

2.宾语从句

He asked her why she was doing that.

3.表语从句

that's why I fall in love with you.

4.状语从句

No matter why she became angry with you, you should  apologise  to her.

二， why 作疑问词 用来向对方问及原因

你我他的提问

A：why are you going to do tomorrow?

why hasn't he brought  the whisky?

why don't you look where you are going?

why can't I remember the exact year we married?

物：

why the clothes are dirty?

PS :http://gaokao.xdf.cn/201109/878805.html

Still confused.