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I agree with Floriane 100%. Add me to the 'me too me too!' pile. This letter describes me almost perfectly at that age (minus the affluent parents and level of sheer cluelessness perhaps).
I also have a 20 year old niece who is almost exactly like Anna - affluent lifestyle, rather clueless, lives in her own world of fantasy books and video games.
Bottom line? There is absolutely nothing wrong with it. As Floriane said so well she'll just learn how to swim. THere is also nothing wrong with showing no interest in boys until your 20s or any other age. Society dictates we must play those stupid social power games in highschool. Those who choose not to participate in those formative years just learn the rules later as I stated. I have many brilliant friends in similar situations, saw highschool drama as pointless and simply kept to themselves, earning the labels weirdo, geek or loner.
It's hard to describe to you 75% extraverted how very hard it is to be introverted in our society. You have to pretend every single day to 'fit in', smile and look happy. When all you want is silence, solitude and time for reflection. Indeed those 'rich inner worlds' (which so many people will scoff and roll their eyes at) can lead to many great carriers.
Here I am in my 30s, great career in the sciences, wonderful husband, dealing with demanding external customers every day with a smile. These are social skills that are LEARNED; it just takes longer for introverts to figure out the rules. Mostly to learn to keep that essential small inner flame alive, and share it with friends through interactive theater, writing, roleplaying, what have you. That's what keeps me sane.
Anna like my cousin will learn this eventually - it will naturally sort itself out. My advise to the LW is to read a few books on understanding introverts and yes, talk to her.