This is such an incredibly huge mistake. When your son’s military career is over, it may very well be the American citizenship he wants to denounce and keep the British citizenship, as he may have injuries from the military that will be cared for in a terrible manner (read horror stories about the Veterans Administration) and face bankruptcy trying to care for his health in America versus trying to get help through the NHS. Even if he’s healthy, American companies often treat their workers like dogs (no sick leave, barely any vacation, barely any maternity leave and no paternity), and I say that not being anti-American. Lots of great things about the country, but in quite a few states, they can just fire you even if you’ve worked somewhere for 20 years with no protection at all (it’s called at-will employment and it’s horrible). Likewise, as a citizen, America is one of only two countries that taxes income you earn outside the country (the other is Eritrea), not the UK. My husband is former US military, we’ve left the US and he is looking at denouncing US citizenship for the tax implications, which are wild. We haven’t run into anyone trying to get rid of British citizenship yet.
Do not let your son possibly face becoming a homeless American veteran when he could also have citizenship in a country that, despite its safety net not being what it was even ten years ago, does have a much, much better social safety net (NHS, council housing, etc). Because it all looks rosy today (he’s an 18 year old supposedly earning $60K and getting an online degree), and in a year, he could be in a wheelchair permanently at age 19 after a single combat tour. It happens every year.