Why do you always milk a cow from the right side?

Tonight Mallory and I were reading a Little House on the Prarie book.  We were reading a chapter called Milking Time.  While reading, Laura was milking a cow from the left side and Ma told her not to do that because the cow would kick her.  Ma said, "Always milk a cow from it's right side".  I looked to Mallory and I asked, " I wonder why you have to milk a cow from the right side?"  Mallory looked at me with the most serious look on her face and said, "OHHH... That's must be because one side is plain milk and the other side is chocolate milk!!"  Well hello, that does sound like a good reason, but of course it isn't.  Do you know why?  We never found out, but we laughed and laughed about it.  She can be so funny sometimes.