Think of it this way, if you're going 100 kts in a no wind situation you travel 100 nm. If the wind is 90 degrees off your course some of your 100 kts gets used compensating for the crosswind and you may only travel 97 nm on course. Even if the wind is 95 or 100 degrees off the nose your correction is going to cost you more than what you gain from the very slight tailwind. Therefore you can prove mathematically that you will have a headwind component more than 50 percent of time while you fly.