From my understanding as the child of a UK-born naturalized American, he exists in a quantum superposition—he both is and is not a British citizen. The US requires you to say you’re giving up your other citizenship(s) when you become naturalized, so Washington would say that he’s a US citizen and only a US citizen. UK law either explicitly says that natural-born citizens can’t give up their citizenship or doesn’t provide a practical means to do it, so His Majesty’s Government still considers him a citizen. You aren’t required to give up your old passport when being naturalized, but applying for a new one or using other benefits of citizenship such as voting has been used against people who found themselves in trouble for other reasons.
Personally, I’m just kind of pissed off that the Home Office won’t let me get a British passport either because they respect the US stance on multiple-nationality or have been pushed into it by a treaty, even though I would be eligible for one in the majority of other countries.