My explanation right now would be that “もう一人でなんでもできるんだ。” does not mean “I’m on my own”.
After posting my previous reply I did a quick google search and found a hinative post where people said “もう一人前だ” could be used to say “You’re on your own”, but I think there’s some confusion going on? As in “to be on your own” having two different meanings: “to be alone” and “to have to do something on your own”. I could see how someone might say “もう一人前だ” to mean the latter in a roundabout way, but not the former.
If you’re going to ask somewhere else, you can always just use the short grammar questions thread. People usually respond there fairly quickly 