This first myth seems to be rooted fairly deeply in the horse world and can make for some heated debates... I hope you enjoy my take...
I think the root of our problem is the traditional treat. Many riders enjoy feeding their horses as a way to show affection. Some riders give a reward at the end of the ride for a job well done. Even when we have a very thought out reason for giving Buttercup a sugar after a great ride Buttercup will not see that same connection.
When you give something as highly valued as food to an animal with no reinforcement schedule in mind (randomly) they will begin to associate the treats with the only thing that is constantly paired with the food reward-your hands or pocket.
Now what happens if you even give Buttercup a cookie when she nuzzles your pocket or lips your hand? You have just reinforced those unwanted behaviours directly! When you look at how most horse people traditionally fed treats to horses you can see where the myth came from. Food does not teach horses to bite. We teach horses to bite.
Another reason I have heard not to hand feed horses is it spoils them. Once again it’s not the food but how the food is being delivered. When you look at how some riders dole out the sugar, carrots, and cookies it does kind of remind you of well meaning parents “spoiling” their children with endless presents. When you give something away with no meaning attached animals and children do kind of develop a sense of entitlement. I don’t have any behavioural backings for this one. It just seems logical. We are all more honest hard working people because we have had to work hard for our rewards right? Life is not about free handouts. Or something like that...
Don’t take my word for it though! Here are some other articles about hand feeding and biting.
Alexandra Kurland answers the question in this interview with Karen Pryor:
(look down the page until you see the question... or read the entire interview it's good!)