This highly dubious, but it's too good a story to pass up!
Before the Battle of Agincourt in 1415, the French, anticipating victory over the English, proposed to cut off the middle finger of all captured English soldiers. Without their middle finger it would be impossible to draw their renowned English longbows and, therefore, they would be incapable of fighting in the future. This famous English longbow was made of the native English Yew tree, so the act of drawing the longbow was known as "plucking the yew" (or "pluck yew").
Much to the bewilderment of the French, the English won a major upset and began mocking the French by waving their middle fingers at the defeated French, saying, "See, we can still pluck yew!" Because "pluck yew" is rather difficult to say, the difficult consonant cluster at the beginning has gradually changed to a labiodental fricative "F," and thus, became the start of the words often used in conjunction with the one-finger-salute! Also, because of the pheasant feathers on the arrows used with the longbow, the symbolic gesture is known as "giving the bird."
And yew thought yew knew every plucking thing.