Romans 13:8-14 calls us to love others, to work for their souls' good rather than looking to please ourselves.
More specifically, verse 10 reminds us that "[l]ove does no harm to its neighbor." Romans 14:1-15:7 offers a discourse on favoring weaker brothers and sisters above ourselves, valuing and encouraging that which is good in the souls of others.
Bottom line: I believe it is difficult and rare — as a practical matter — to honor these principles in the context of a close, intimate friendship between two single Christians of the opposite sex.
(For the verbally precise among you, I think such friendships between non-single Christians are also a bad idea, but that's not what we're talking about here.) Intimate friendships between men and women almost always produce confusion and frustration for at least one of the parties involved.
Would want to date someone knowing that he or she had a significant, pre-existing and ongoing emotional bond with another single member of the opposite sex?