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Unless she's grossly exaggerating, of course. But most of you here seem to assume she's not, and are busy attacking her and saying "poor child". Phooey.
I'm not saying to hate on the child. But if the description is at all true, it sounds like there is actually something wrong with her. Asperger's maybe? (Someone said that already, just not enough of you. I agree totally.) And sorry, but I would not want to take care of such a child either. Maybe it makes me an awful person - I just think it makes me honest. I'm not claiming she's unlovable, I'm claiming Anna takes more care than this LW is able to give, and there's noting wrong with that. Whether the child is completely "normal/healthy" or whether she has needs, LW doesn't have to want to inherit what sounds like a 5 year old in a 16 year old's body. No way will this girl be able to go out on her own life in a couple of years.
LW - sorry to say but I believe you must leave this man. I thin it's best for her and best for you. If you're not ready to do that, than good for you. But you must sit down with him and tell him exactly how you feel. You must say "I am dedicated to you, and I want to love Anna. But I'm not feeling ready. I'm feeling that she has really big problems that I am not equipped to handle. I need your help to find the best solution." That, in my opinion, is what you do with problems with someone you're considering marrying.
That being said, yes LW, realize what a terrible father this guy is. He's either been so deadbeat that his daughter has been grown up to seem like she was raised by wolves OR he's so deadbeat that he has failed to have her perhaps obvious health issues diagnosed. Neither option makes him look like a very promising partner in the long term, if you desire any kids of your own. You may love him a lot, but be brutal in judging him as a lifelong partner.
But really. LW is exaggerating or Anna is mentally disadvantaged somehow. Also for the sake of the child, one should figure out which is true so she can get what is actually the most proper care/treatment.