If one assumes that homosexual attraction is innate (which twin studies demonstrate pretty clearly it is not, at least at birth), that still does not mean that engaging in homosexual acts is not a specifically chosen behavior.
A person is heterosexual when they are sexually attracted to the opposite sex, not because they have sex with members of the opposite sex. The same type of definition should apply to homosexuals. People who are free to choose are not going to engage in an activity that they don't already find attractive.