Cook neither denies or affirms anything about his sexuality or any relationships. He has never been photographed in the company of any particular male or female. It's possible he's married to the job regardless of his sexual orientation. One photograph purporting to shoe Cook with a male is an obvious photoshop fake, placing Cook's face and head on someone else's body.
I remember when Jobs died that the reports were quite open about Cook.
“Cook neither denies or affirms anything about his sexuality or any relationships.”
That is a civilized way of being open.