There is a same sex reality and possibly several same sex realities. But first I have never had a therapy session center on a hug or hugs. I understand hugs to indicate "warm fuzzies." Same sex warm fuzziness consciously screams self love and love of self whispers of narcissism or possibly homosexual tendencies. The love of self is proper and homosexuality is a valid and recognized sexual orientation.
Narcissism can be complicated but it is treatable. So Freud wasn't always right and everything is not sexual. However, one must eat to survive and one must survive to have sex and one must have sex to sustain and propagate the human population. Everything else is extrapyramidial. All of this in a same sex hug. As a child man's first love was a woman, as a child woman's first love was a woman. Woman, the first harbor of life and first server of nutrition.