Some think it's jealousy. However, that's attributing human emotions to chickens, and it's somewhat doubtful chickens experience true jealously which is pretty complex even for humans experiencing it.
It's more likely that by picking up a chicken, you are calling attention to that chicken and making them a target of the aggressive members of the flock. It's even worse for that chicken you have picked up to hold them while within range of these more aggressive members. These chickens then quickly recognize that chicken is unable to evade attack by running away, so they capitalize on the opportunity to show their dominance over the captive.
If you are fond of a particular chicken who appears to enjoy cuddling, try to make it a positive experience by showing your affection out of range of the dominant chickens.