Health for all children is an ideal, something we would find in a utopian society, which does not exist. It's a laudable goal, and a good one to have nonetheless, since it motivates us to strive towards continually improving overall health, not to treat any health issues as acceptable, or to exclude any population from health improvement efforts.
If the focus of the question is whether or not all children can be healthy or in perfect health, I would say that clarification is needed. For example, if a child is born with a condition, does this make them unhealthy? If a child is born hearing impaired or with Downs' Syndrome, or if a child is born HIV Positive or born with Asthma, would this qualify them as "unhealthy?" Are we including mental health or simply physical health? Along these lines, are we suggesting that health care opportunities and alternatives be provided to all children? I think that more clarification is needed on these points as to what defines "health." I suppose I would argue that anytime the word "all" is included in such a statement, difficulties arise. It is very challenging to ensure that "all" of anything is met or achieved. Yet, in this case, I would say that "all" should be a goal to which every adult must be committed. Indeed, it should be seen as possible for all children to be healthy. I would think that all adults have to see themselves as vitally invested in the drive for all children to be as healthy as possible. There should be a belief that all children should be healthy, can be healthy, and can be helped to be healthy. Additionally, I would say that health care opportunities should be afforded to all children and this should be a goal and reality to which one should drive.
I agree with all the comments above, I would only add that one factor that would contribute to achieving health for *all* children, *globally*, is sensitivity to local cultures, awareness of local economic factors and , most importantly, to people's perceptions( their willingness to contribute to the health of their children, their willingness to accept the scientific theories of curing ilnesses). For example, in some cultures, schizophrenia is seen as a spiritual gift, a talent which only some people/children get in order to communicate with other 'dimensions'. In those cultures, people would be very reluctant to take their children to the doctors to get medicines for this illness.
The phrase "health for all children" sounds like some objective or program of some government agency. Viewed this way it would mean the availability of adequate nutrition, healthy living environment, and adequate medical attention to all children in a country or a society. This is definitely an achievable goal, and a goal that is worthwhile trying for. However it must be understood that it is going to be a very difficult goal to achieve for most of the countries, and it may take many decades to achieve this goal. Currently there are limitations in the medical systems of the most affluent nations of the world also, and they also need to improve their medical system to achieve the goal of health for all children. The developing and poorer nations have a much longer way to go.