關於英文insist on my的問題。?

"insist" as appearing in the sentence is an intransitive verb.

"insist" + preposition "on" is a kind of phrasal verb to be used to demand that something should happen.
~ insist on something (noun phrase)
~ insist on somebody (X) cannot be used, as there is no meaning at all!
~ insist on doing something (gerund phrase)

** We can put a noun or pronoun in front of a gerund to show who or what is doing the action in the gerund.
~ In formal writing, we must use possessive case;
~ In informal writing, it is acceptable to use a simple noun or an object pronoun instead; and
~ there is no difference in meaning in most of the cases between the possessive form and object form.

That said,
1. He insisted on my going with him. (formal writing)
2. He insisted on me going with him. (acceptable as informal use)
Both sentences have the same meaning!

However, it will not be the case for some transitive verbs as the meanings will be different.
For example, the transitive verb "like";

~ He did not like the woman standing in front of him at the parade. (participle phrase)
(= he didn't like the woman who was standing in front....)

~ He did not like the woman's standing in front of him at the parade. (gerund phrase with possessive case)
(= he didn't like the fact that someone (the "woman") was standing in front of him at the parade.)

Obviously, the above two sentences have different meanings.

簡單的說。
insist on + 名詞，而insist on "強烈要求"的標的物是going 這動作，不是"我"，因此"我"不可使用受詞，而"我"`字是用來修飾"going"這字，故應寫成"我的"。

即他堅持"going"`，但是誰的"going"? , 是"我的going",故是my going".

my=possive adjective
me=objective case;
my going with him=noun phrase;
meaning possess and insist by him as the subject.
Hence :-He insisted on" my going with him."

insist 是不及物動詞需加介詞on形成及物動詞，而介詞後需使用名詞，其中my是代名詞當形容詞修飾動名詞going，with me 是介詞片語當副詞修飾動(名）詞
為何不能說He insisted on me.應為語意不完整，他堅持我但不知做何事？假如寫成He insisted on me to leave. Ok 意思完整了。

1. 要是海倫王真正聊解這句話的意思,答案就很明顯了.

主詞"他"所堅持的是<神東東>呢? 是<我>這個人呢?還是<我跟隨著去>(這件事)呢?

要是 海倫王 認為是前者的話,就應該適用"me".

要是 海倫王 認為是後者的話,就應該適用"my going with him"(名詞片語當受詞).
但是在一般場合中,二者都有人說/使用上都是一樣的.

2. 其他例子:
當主詞:
my studying in politics cost a lot of money.

3. 其他說法:
He insisted that she go.
醬子的說法 是比擬的原句還要普遍/好懂.

4. 聰明的海倫王 一定會續問 "那要是堅持的對象是<我>" 要怎說呢?
因為 沒問,我就不說了!