Got it.
That white is a connective membrane holding the main part of the breast and the tender together. It's often called "silverskin."
Depending on how you prepare the chicken, you can leave it or not. It disappears when baking, roasting, or frying.
Most of the time I remove it, because I separate the breast and the tender. Most people do not, and leave it in place when cooking a whole breast.
There is a tendon inside the tender that also disappears when cooking. But for many applications I remove it, too.
So, the bottom line is, there isn't a right nor wrong about this. It just depends on your personal style, and how you prepare the chicken.
How old is your daughter? If she's young enough, you can just tell her, "because."