What was this body part? This is the answer submitted by a listener:
Dear Click and Clack,
Thank you for the Agincourt 'Puzzler', which clears up some profound
questions of etymology, folklore, and emotional symbolism. The body part
which the French proposed to cut off of the English after defeating them
was, of course, the middle finger, without which it is impossible to draw
the renowned English longbow. This famous weapon was made of the native
English yew tree, and so the act of drawing the longbow was known as
"plucking yew".
Thus, when the victorious English waved their middle fingers at the
defeated French, they said, "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
lover pheasant plucker", which is who you had to go to for the feathers
used on the arrows), 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 to arrows that the symbolic gesture is known as
"giving the bird".