We see people doing these all the time, often they have heard that the exercise is not recommended but continue to do them anyhow. Who recommends against these? NFL trainers, the Mayo Clinic. I'll give you a link to the sources and summarize below.
Over time, performing pull downs behind the neck weakens the rotator cuff - you probably won't feel this immediately but weeks, months or years later you'll pay a high price, According to NFL trainer Dan Riley, this exercise puts the shoulder and specifically the rotator cuff muscles in a weak and vulnerable position. The shoulders are forced to rotate externally and the shoulder blades move to the center of the body, causing the external rotator cuff muscles to pull against the tight internal rotator muscles. If you work at a desk all day long your shoulders are internally rotated and the internal rotators are TIGHT! They simply are not made to bear this weight and stress. Over time they become weaker or fibrous, injury follows, and you can kiss your rotator cuff muscles goodbye. There is also risk to the cervical spine from bringing the head forward. Plus, this exercise is not even as effective in targeting the lats as pulldowns in front of the body.
Behind the neck shoulder presses and upright rows are two other exercises that should be avoided for the same reasons. When performing pulldowns and presses, keep the weight in front of the body.
Click to view a video on proper technique from The Mayo Clinic.