My most charitable interpretation is that they think moving = citizenship and a LOT of people have somehow have only heard of the cases where people have to choose between citizenships, not the ones where they go on with life with two passports. My group of friends is from all over though so I'm very used to it being completely a non-issue to be dual (or more) citizens, while the people who say these things tend to run in very non-diverse circles. I think those two issues combine to explain most of it, but I still don't get the part where we have to do something to maintain US citizenship like it's some use it or lose it thing.
I don't think it's about disapproval because most of the time it's actually been from supportive people.
I do think if this idea of how citizenship works is as widespread as it seems based on my experience, that could explain a fair amount of the flack we (general we here) get for this move. I can understand why people would be pissy about someone throwing out their US citizenship (especially as they follows that we'd be deciding that for our kids and would be making access to family in the US more difficult). It's just that, of course, it's a completely made-up line of thinking that somehow a lot of people seem to believe. Now I know that with my husband's family it mainly comes from the cousin in Mexico but the rest are a mystery. I think I'm going to start asking why people think that instead of jumping straight to the "no, we have to beg and pay off the government if we want to drop our US citizenship" thing and see if that explains any more. Maybe a lot of families have some rando distant relative who "just can't leave Mexico due to paperwork the US requires"