Why was hes so annoyed when he said she could stay?
When she went back with him after they first met he said shed could stay.
She was seriously annoyed/insulted by this.
Obviously it's understandable that she may not have wanted to - indeed that she may have had very strong feelings on the subject - but in this day and age it seems odd that she should have been so offended. Particularly because there are occasions when you meet someone and feel such a strong connection that you just don't want to part from them (because you feel that after such a short time you may lose them once you say goodbye) and his main intent may not have been sex but just to keep her company (which is rather how it came across to me).