Am I allowed to have friends of the opposite sex

my present ex-fiancee blamed me for a relationship failing since I had/have many online female friends. And that is all they were friends. Most of my female friends are from out of state. My ex fiancee complained even about my friends on my facebook who I went to high school and college with, my take is "if they didnt want to date me then, why would you want to date me now". My question is this (and this is her point of view):

- two people who are in a relationship *cant* have opposite sex friends who are single because they maybe some sexual undertones to it

- a person in a relationship cant have have a single male/female friend, and go out to dinner or out for coffee with them,without another person of a different sex because of sexual undertones

- a person in a relationship cant have friends of the opposite sex because of the same points above.

This was an ongoing problem in the relationship and has festerd into countless fights. Am I wrong for having female friends (when the female friends knew full well I was in a relationship)