I don't know DS but my guess is, Singapore doesn't recognize dual citizenship, hence you must renounce your US citizenship to get a Singapore passport.
That's correct. In fact Singapore is so against dual citizenship that even people who have dual citizenship by birth must choose one or the other once they become adults: by age 22 they must renounce all other citizenships, or lose their Singapore citizenship.
Denmark is another country with a similar law, which causes a reasonable amount of angst among Danes reaching that age. Particularly true of those with US/Danish citizenship, because once you renounce one or the other, it closes off a lot of options: being a US citizen can be quite good for a lot of career paths, while being an EU citizen can open up a lot of options in a different direction.
edit: Looking into a bit, one thing making Denmark's law somewhat less draconian is that former Danes who lose their citizenship via this process at age 22 still have some kind of special lifetime Danish work/residency permission. So they could opt for the U.S. citizenship while retaining the option to return to Denmark. They would lose the right to live/work in other EU countries under the freedom-of-movement agreement, though, since they'd no longer have an EU passport.
Are there any other EU countries that (1) a young Dane could reasonably obtain citizenship from, and that (2) do not require renouncing other citizenships? The idea is that a dual US/Danish citizen approaching the age where Denmark requires renouncing one or the other could obtain some other EU citizenship first, and let the Danish citizenship go. He'd still be able to live/work in Denmark as an EU citizen.
I can't seem to find discussion of it being done, so perhaps there's some barrier I'm not aware of, but I believe Sweden should be a plausible route for that. A Dane who lives in Sweden for at least two years is eligible for Swedish citizenship under a special citizens-of-other-Nordic-countries fast track, and, since 2001, Sweden permits dual citizenship. In addition, since 2000, the Øresund Bridge makes it possible to live in Malmö, Sweden, while working in Copenhagen across the strait, so you don't even have to fully move to Sweden, just sleep there.
Belgium, Finland, France, Ireland, Portugal, Sweden and the United Kingdom all permit naturalisation without requiring renunciation of previous nationality. This list is not exhaustive.
Same for Japan unfortunately. Although there is a growing trend of just ignoring the notifications and being careful with your passports... it's been fine for a number of people I've talked to, but I'm still curious as to how easy it would be for customs to find out.
Denmark is another country with a similar law, which causes a reasonable amount of angst among Danes reaching that age. Particularly true of those with US/Danish citizenship, because once you renounce one or the other, it closes off a lot of options: being a US citizen can be quite good for a lot of career paths, while being an EU citizen can open up a lot of options in a different direction.
edit: Looking into a bit, one thing making Denmark's law somewhat less draconian is that former Danes who lose their citizenship via this process at age 22 still have some kind of special lifetime Danish work/residency permission. So they could opt for the U.S. citizenship while retaining the option to return to Denmark. They would lose the right to live/work in other EU countries under the freedom-of-movement agreement, though, since they'd no longer have an EU passport.