I shared this teaching with students recently and have gotten LOTS of interesting feedback from girls and guys alike. I hope this helps you as a parent.
First, it's dangerous for guys and girls to be BEST friends. Girls need other girls to bounce ideas off of, get advice from and to encourage them in the way they should follow after Christ. I get that idea from Titus 2:4-5 where older women are taught to have their heart turned toward their own home, and THEN TOWARD OTHER WOMEN. Women are instructed to teach and connect with younger women. On a practical level, a young man who is BEST FRIENDS with a young woman is in dangerous territory (unless they are married to each other). The young woman's heart is won over by friendship/emotions. Also, I have seen SEVERAL marriages END because the husband became great friends with another woman at work, or the wife began to share her marriage problems with another man ("who had a listening ear"). If we don't make the distinction that guys should be BEST FRIENDS with other guys and girls should be BEST FRIENDS with other girls, we are setting up some marriages to fail.
Second, until someone gets married they should identify MOST with their own family, not other students--especially opposite sex students. A young man should act and think how his parents think until he gets married. Even if you go off to college, I want each to be thinking from their parent's perspective about how he relates to girls, what he does with his time, how much effort he puts into studying, what he posts on facebook, etc. I get this concept from Genesis, which says that the only reason that a young man LEAVES his family relationships (identity) is to "cleave to his wife" (check out Genesis 2:24). Young girls should also identify most with their family, not with some exclusive dating relationship. She should be understanding her dad, and getting advice about life from him and other family members. I know that many families don't have a dad who cares (or who follows God), and that's where things can get tricky. That's what the church is for (and those other female-female relationships I mentioned above).
Third, the pattern of Scripture puts forth examples of same sex friendships being best friends, but never of opposite sex relationships being best friends, except within marriage. Naomi had Ruth. David had Jonathan. Paul had Silas and then Barnabas. Jesus hung out with the 12 disciples--all men. He knew women, and even called them friends, but they were not His closest friends. Where there exists examples of opposite sex close friendships, they are FAMILY ORIENTED (like Mary, Martha and Lazarus, Esther and Mordecai, etc.).
Fourth, young men should treat all young Christian girls as sisters (1 Timothy 5:1-2), and none of them "differently" from the others. It's that special treatment that confuses a young girl and makes her think that something is there that may not be. This is a crucial point, for I AM NOT SAYING THAT GUYS AND GIRLS SHOULD NOT BE FRIENDS--THEY SHOULD BE FRIENDS, JUST LIKE YOU ARE FRIENDS WITH YOUR SISTER. I am saying that they should not be "share-everything" "best friends." So Christian guys should be friends with LOTS of young Christian girls and treat them all the same--as sisters. This is also how you find out what you really like in the opposite sex, and what drives you crazy--it helps you make the choice regarding who will be the ONE female BEST FRIEND, when the time is right.
Fifth (and finally for today), the reality is that each Christian man is completed by becoming BEST FRIENDS with JUST ONE CHRISTIAN girl in marriage. A Christian man will be best friends with one girl for life someday. I am best friends with my wife. I share stuff with her that I don't share with anyone else in the world (Genesis 2:18-25)--not even other men. God "brought her to me" and she completes me. You are designed to have one best friend of the opposite sex when the time is right. That's a fantastic thing!
A young Christian man is becoming ready for that relationship when he is treating all Christian girls as sisters and when he begins to have a life to share with one of those girls.
Don't offer to share your life until you have one.
For additional reading: "I Kissed Dating Goodbye" (Josh Harris) contains some of these concepts. I believe every Christian parent should be familiar with the concepts Josh advances in this book.