An anecdote (please, help me with this text)

Last year I met with an English girl because I wanted to practice my English. One day she asked me about going to the cinema and I accepted. On our way to the cinema, we went by the door of a hairdresser salon. She told me that at the beginning of her stay in Spain she thought that a hairdressing salon in Spain was a place where films were screened because the word “peluquería” in Spanish has the same root that the word “película." I challenged her to go into a hairdressing salon and ask about the films that were being screened there, but she didn’t do it. It is a silly story, but it makes me laugh and I think that it likes me because that girl is as innocent and kind as this story.

"that it likes me"  I don't quite understand what you were trying to say here.

You could just say "... it makes me laugh and I think that she is as innocent and kind as this story." 

Thanks for sharing! I love hearing about the little confusions that occur when learning a new language. 

Hope this helps!