I think when people say to "take emotions out of it," they mean that something must be done/believed despite our feelings against it. I agree with you that emotion exists in some degree with anything, but, I think the categories of emotion, thought, perceptions, belief, instinct, etc., have some overlap and blurred boundaries. Some people say, "I feel that..." while others say, "I think that..."
I do think it's possible to take the focus off a particular emotion, let other parts of the brain kick in, and then a more suited emotion will come in eventually. But, it's not so easy as just deciding to make that process happen, sometimes.