Advantages of NOT being a citizen? In his case, not much I can think of except these few (for others the pros and cons are different because of their original country's rules regarding dual citizenship):
- If he leaves the US and officially surrenders his green card, he can escape the ongoing worldwide taxation that would apply if he became a US citizen*. If the departure is before 8 years** as an LPR, he would also escape the special expatriation tax (which may apply to those whose assets total over $600K of capital gains).
- He doesn't have to serve jury duty (except maybe in New York, where I've heard they've started requiring permanent residents to serve)
- It is not safe to be American when traveling certain parts of the world (although if he travels with you he might be perceived as American anyway).
*for very wealthy permanent residents (I think over $2M net worth) who leave without becoming citizens, they still continue to tax them for some number of years after they've left the US. Of course, enforcing it can be difficult or impossible if the person has no US-based assets and doesn't visit the US.
**for the purpose of this tax they count a single day in a calendar year as a whole year, so it doesn't mean 8 full years.