Many years ago, the title of this article was almost a famous song, featuring both as a stage musical number and, later, as a free-standing pop or blues song. For the obvious cultural reasons, it reinforces the link between hats and the head. From the earliest times when clothing was just being invented, humans found various good reasons to cover their heads. It's a good way to prevent sunstroke or, at the other end of the temperature scale, to keep frostbite from removing ears and noses. When status and rank became more important, headwear indicated who was thought important. Later, it became the means of concealing hair loss. Even in the earliest centuries, men have always been embarrassed when their hair thinned and dropped out. Not all societies venerate age. This can make it important to conceal balding as one of the symptoms of aging.
The problem, as always, is to decide whether the means of concealment make the hair loss worse. Modern experts will tell you wearing any type of hat does not damage your head. Yet there's considerable mythology from the military where uncaring sergeants make the recruits wear those terrible helmets. This is not to suggests previous wearers were infecting the newbies with hair-eating fungus, but to suggest that many volunteers are entering the military at a time when early hair loss might start. In practical terms, there's no connection between what you wear on your head and the decision made by your genes to start your hair thinning and dropping out.
With this general reassurance ringing in your ears, if you absolutely feel you must cover up hair loss as it starts, it's probably better to wear a hat that does not pull at your hair as you put it on and take it off. Propecia is reliable in almost all cases of Androgenetic Alopecia. As soon as the hair loss has slowed and you grow more confident about your appearance, you can wear the hat less often. As to the Propecia, you have to keep taking that.