Sentence Correction

In contrast with the way he argued with his parents, Jonas was actually quite happy about his having to go away
to camp for the summer.
A. his having to go away to camp for the summer.
B. him having to go away to camp for the summer.
C. his having to be going away to camp for the summer.
D. himself having to go away to camp for the summer.
E. him having to be going away to camp for the summer.
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correct answer is (A).

the question tests gerund.
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Deb


In my opinion, “his” is a possessive pronoun and “having” is an object of the possessive pronoun (his). Therefore, “his having” becomes an objective of preposition (“about”).
This is how I understand this question and answer (if the correct answer is A).
However, according to the answer explanation of OG-SC-19, it said that “the ~ing form of a verb can be used as a noun, but it is often awkward, particularly when used with a possessive.”
On the other hand, as you see this question, we can use the ~ing form with a possessive as correct grammatical construction.
Which rule should I follow to solve SC? Can anybody explain me?