This reminds me of David Reimer who was a part of the study that became known as the John/Joan case in the 60's and 70's.
After a botched circumcision, David was resigned as a female and later reasserted himself as a male later in life. He eventually ended up committing suicide at 38. Much like David's parents, these parents are also imposing a gender identity onto their children.
You tend to see this sort of thing happen with parents who subconsciously want a child of the opposing sex. Like if a parent wanted a boy they teach their girl how to box and play baseball. Because in their mind, boys like to fight and play sports.
To enroll your children in activities not normally associated with a specific gender is fine and should be encouraged. Keep in mind that in doing so you are influencing their future taste, preferences, and behavior. That girl may one day grow up to be an aggressive/assertive person based on the nature of their upbringing. She is acting that way because of how she was raised, not because she was assigned the wrong gender at birth.
