Miss Wang sent me a private message asking me to comment on the following. So here we go:
# He insisted on to read the letter.
Why is this grammatically incorrect?
It is incorrect because after "insisted on" we need to use a participle, "reading", and we cannot use an infinitive, "to read".
# He insisted on having the letter.
Why is this not the right choice?
It is not the right choice because prima facie "having" means "taking possession of", and this is not the story (however sketchy) that Miss Wang told us.
I hope you are happy, Miss Wang, now that I have complied with your request.