"Every other developed country has some kind of universal health care, so we should probably have it too" is one of the arguments for universal healthcare, but it's not the only reason, because it's certainly not true that we should do things simply because other countries are doing them.
It's the same kind of reasoning as "all of my friends that are really well-off are investing, so it would probably be a good idea if I did too". There are arguments for investing besides the fact that all your well-off friends are doing it, and investing's worth isn't derived from the fact that your friends are doing it; however, the fact that all your well-off friends are doing it provides support that it's a good idea.