I'm a dual citizen with 2 passports. Let's say passport A and passport B. Passport A is the country of birth / country of origin. Passport B I acquired later in life before immigration to US.
Upon entering US I presented my greencard and was fully prepared to also show my passport. When asked to show one I showed my passport B. I was then surprised that the immigration officer didn't accept the passport B and asked me to present passport A. When I asked for the reason the reply was look at your green card (where the country of origin is) it says Passport A, you have to show me passport A.
I was under impression that I am entitled to show any passport as long as I have at least one I should be permitted to enter is that not true ?