Although parents cannot be best friends or very good friends with their children because of diffrence in their thinking, but they can still be a kind of a support for sharing your feelings, especially for children who have crossed their teenage. Yes, i strongly believe that parents cannot be friends with their children until the children cross teenage and reach a certain maturity level, because then they can both understand each others opinions.
I believe a parent cannot be your best friend. This is especially for teenagers. Parents need to remember that their roles are to discipline their children and teach them right from wrong. That would be hard to do if you are "buddies" with your child. Maybe later in life parents and children can be friends, but not when the kids are young.
A parent's job is to parent. This requires a certain amount of authority. While parents can be friends with their children, being best friends requires them to relinquish the necessary authority to provide proper guidance as parents, since best friends are usually consider themselves level with each other. It is, therefore, not only not possible for a parent to be a child's best friend but inappropriate.