If you really want to understand what may be going on here, I would recommend that you read the "For the Strength of Youth" manual. 
 
For the Strength of Youth 
 
In particular, take a look at the section titled "Dating". This will explain the standards that she is trying to adhere to. 
 
In a nutshell, LDS youth are counseled to not date until they are at least 16 years old, and even then, they are encouraged to not date exclusively but go on group or double dates. They should also only date those who hold high moral standards like they do. The first several years of dating really should be more focused on building good friendships, developing good social skills and enjoying wholesome activities rather than trying to find one's soulmate. 
My advice to you regarding this particular young woman would be to not worry about becoming her boyfriend. Concentrate on just being her friend. That is what she most needs at this point in her life, good friends who will help her hold to the standards that she holds dear. You will find much more satisfaction in a good friendship at this stage of life than you will in an exclusive romantic relationship. Just give it time, be a good friend, and trust God. If the relationship is meant to be and you keep yourself worthy, it will happen in the Lord's time.