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performance anxiety and fear of looking stupid as a beginner as completely separate thingsThe same kid will happily try riding a bike if you just leave one sitting around where they can find it, but will balk if you ask them to try in front of their friends who already know how. I think a huge part (the majority) of people’s fear of learning new skills is a kind of performance anxiety. Both fear of looking bad in front of others, and to some extent fear of looking bad to themselves. The other significant problem is an inability to break the new skill down into small enough pieces to manageably tackle independently.
Speaking a language is always and inevitably a performance. But kids are typically given much more time and space to just listen without trying to speak, and are judged less when they do try. Some kids who move to a new country will just quietly listen for months before ever trying to say something in the new language; adults rarely have that luxury.
But in any event, there are plenty of adults who are willing to try speaking foreign languages imperfectly, and studies have shown children and adults have comparable ability to learn a second language (indeed adults often improve faster at the start).