I don't think there's any sort of "stigma." There's just the fact that, since "old people"
are on Facebook—and that likely includes your parents and other relatives—they all expect you to add them as a Facebook friend. At which point you won't be able to be yourself on Facebook any more, because they can observe any of your "broadcast" activity.
The nice thing about the other platforms isn't that they don't have "old people" on them. It's specifically that your parents and relatives won't even think to add you on, say, Snapchat.
Also note that the apps that teens mostly do interact with parents through now, consist mostly of group-chat apps like Messenger or WeChat, where there is an explicit separation of social contexts (the groups you're chatting with), such that you don't need to worry about your relatives seeing anything as long as you don't put it in your family group.