This is not meant to be crude. It is strictly for your edification and enjoyment.
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 the middle finger, it would be impossible to draw the renowned English longbow and therefore be incapable of fighting in the future.
This famous weapon was made of the native English Yew tree, and the act of drawing the longbow was known as “plucking the 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! PLUCK YEW!”
Over the years, some ‘folk etymologies’ have grown up around this symbolic gesture. Since ‘pluck yew’ is rather difficult to say (like “pleasant mother pheasant plucker”, which is who you had to go to for the feathers used on the arrows for the longbow), the difficult consonant cluster at the beginning has gradually changed to a labiodental fricative ‘F’, and thus the words often used in conjunction with the one-finger-salute are mistakenly thought to have something to do with an intimate encounter.
It is also because of the pheasant feathers on the arrows that the symbolic gesture is known as “giving the bird”.