The phrase isn't about physical solitude but about making decisions without external influence. She decided to travel alone to Europe to be her own woman.
Pro Tip 2/3
Emotionally Positive
It often has a positive connotation, implying admiration for someone's independence. He admired how she would always be her own woman, despite the pressure.
Pro Tip 3/3
Not Always Solo
Independence doesn't mean one always rejects advice, but is selective in considering it. He is his own man, yet he listens before making his final decision.