They may want to have different standards for their children than for themselves. There are 4 main components to the privacy on Internet issue. The notice provided, however, doesn't really give the user sufficient information as to what the cookie will actually gather as information or provide the user as a benefit. Further, once the user grants permission for the cookie, the site will not ask again until the expiration date of the cookie as defined by the web site. In other words, it is hard to change your mind.
Cookies do provide benefits to users.
If you are a frequent customer of a particular web site, you might want to have a cookie saved with your recent transactions, or your general color preferences or whatever information might help the vendor better serve your needs. However, users also want control over what information is gathered and how this information will be used. Parents may want a greater degree of control over the information gathered and used about their children. The current implementation of cookies is not sufficient in this regard. This allows the consumer to make an informed choice about whether he wants the value provided by the cookie.