Dad shows are about real men with real-man problems
While there are some shows with female protagonists that come close to dad show territory, anything too preoccupied with female concerns is not a dad show. In general, dad shows center around a male protagonist dealing with typical dad issues, such as not connecting with his kids, lack of fulfillment at work, middle-aged financial burdens, stunted emotional growth, and marital issues as seen from the male perspective. Their character descriptions often sound like this: "Widowed only a year, Longmire is a man in psychic repair that buries his pain behind a brave face and dry wit."
"There has to be an ultra-masculine, kind of quiet main character," offers my Thrillist colleague Kevin Alexander. "Preferably one who doesn't talk a lot, but when he talks, says meaningful things, and knows how to handle himself in a fight, and likely owns a pretty weathered leather jacket. All dads want to be able to pull off the leather-jacket thing, but they know they can't."