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What Are Our Mirror Reflections Trying to Teach Us?
People whose personalities and actions tend to push our buttons the most are generally our greatest teachers. These individuals serve as our mirrors and teach us what needs to be revealed about ourselves. Seeing what we don't like in others helps us look deeper inside ourselves for similar traits and challenges that need healing, balancing, or changing.

When someone is first asked to understand that an irritating person is merely offering him a mirror image of himself, he will strongly resist this idea. Rather, he will argue that he is not the angry, violent, depressed, guilt-ridden, critical, or complainer person that his mirror/teacher is reflecting. The problem lies with the other person, right? Wrong, not even by a long shot. It would be convenient if we could always place the blame on the other person, but this is not always so easy. First ask yourself "If the problem truly is the other fellow's and not my own then why does being around that person affect me so negatively?"
http://healing.about.com/cs/selfactu.../a/mirrors.htm

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Encoraging and appreciating a child's uniqueness, imo, is not what is being called "mirroring" here. Joining in and doing exactly as the child does is more like mirroring...speaking to them as they do to us etc. IMO