It's of no use to argue with him. 請問這句話中,of的用處是什麼?

1.) It's (of) no use to argue with him.
在平常的情況下，of 是可有可無。
http://dictionary.cambridge.org/dictionary/english/be-of-no-use
但這是非常粗淺的理解。因為多數人早已混用

2.) be of + noun 的使用源自早期典雅的英文。時自今日，某些用語成了慣用語 (idiom)，多數時候則是較正式的用法，如法律文獻就偏愛 be of + noun
http://english.stackexchange.com/questions/47382/meaning-and-usage-of-be-of
(所謂 "正式" 的用法，套句中文的解釋就是"文謅謅"

3.) 幾年前，我看到有人說 加上of ，是將形容詞轉成名詞的寫法，這是知其然，不知其所以然
It's of no use to argue with him. (no use 強調對整個情況situation 無濟於事)
It's useless to argue with him. (useless 是個形容詞，這時語意則傾向他是無可理喻的)
使用名詞或形容詞，在整句話中是有所差異的。在一般人的日常使用上，也許無甚差別。在外交辭令上，就可能造成情勢完成改觀。

參閱:
https://forum.wordreference.com/threads/be-of-noun-v-s-be-adjective.1372260/
https://forum.wordreference.com/threads/to-be-of-noun-vs-to-be-adjective.3105636/
https://forum.wordreference.com/threads/its-of-no-use-to-do-or-doing.2409047/

You use of to indicate a characteristic or quality that someone has to introduce a person that has a particular quality after verb to be.(=is)
eg:-of its kind
-----of no use
-----of his own;
It s of no use to argue with him
=Don t argue with him.
=a matter of no importance
=a matter of no use
=showing the cause, with Or having
=a preposition.

本句it是假主詞，而真正(遞延）主詞是to argue with him。
is 是不完全不及物（連繫）動詞，需接主詞補語，所以需加of形成介詞片語，加of.是表示有……特質。
不加of的條件，除非是同位語，例如:He is John.