whose 和名詞子句的(that)差在哪裡?

The idea that you can persuade him is wrong.
名詞子句that you can persuade him是限定性質的「同位語」，對前面的普通名詞idea的範圍加以約束。that 是引導同位格名詞子句的「連接詞」。

上面的名詞子句有自己的主詞you。
whose沒有「連接詞」的功能。在「文法」和「語意上」都不能用在這句來取代that。

whose是「疑問代名詞who的所有格」。
1.可當形容詞用：Whose umbrella is this?
2.可獨立使用：Whose are these shoes?
3.當關係代名詞用：I know a girl whose mother is a pianist.先行詞為人，帶出形容詞子句當作修飾語（限定性質，不用逗號隔開）。
A book whose pages are torn is worth less money.先行詞為物，用法同of which也是帶出形容詞子句當作修飾語。
Mrs. Brown, whose house we have rented for our vacations, is a rich widow.
形容詞子句當作「非限定性質的修飾語」（前面要加逗號）。

(A)which---rel pro, obj of idea, not as subj of idea in the clause.
(B)rel noun clause used in defining to "that" for idea,,as a conj introducing noun clause and kept here, coordinating to noun cl as conj. to follow "idea" as the noun clause..eg:_Persuade=to cause to do something by reasoning, arguing, begging, etc.It means to try to persuade him.You persuade him into nothing.You cannot persuade/convince/influence him.------------correct
eg:-The trouble with the idea is "that" you are wrong in the power of persuasion.(n)
(C)whose---poss pron of whom, in rel defining clause is used in place of which but different construction as eg:-the idea whose convincing reasons are wrong, are persuaded by you.
(D) by that:-is an adverbial phrase of manner cannot follow the noun"idea" or part of the idea.