(that)you don't like him is none of my business为什么不是whether

(that)you don't like him is none of my business 你不喜欢他不关我的事
这个句子中,可以这样理解,把you don't like him这个插入语拿掉,
?is none of my business.缺主语,用what是缺宾语,这句子不缺宾语,who是谁,完全行不通,whether是引导条件状语从句里用的,用这三个词都不能使之成为一个独立完整的句子,只有用that

That is none of my business.而you don't like him是来补充说明that的