If a child is taught not to do evil, then he will possibly remain neutral - a fence sitter. However, this does not mean that he is no longer capable of doing either the good or the bad. He/she will just be more inclined on not performing evil deeds.
If a child is taught to do good, then he will continue making changes guided by values he chose to live by. The changes he/she makes may not hold a great impact, but a contribution non the less. This, however, again does not mean he is no longer capable of having twisted values that may actually be counterproductive to society (ie. Having Absolute beliefs that result to wars; Adolf Hitler)
The definition of good and bad in this debate are highly cultural, but still has to follow the universally accepted moral norms.
It's actually better to tell someone to do the action you want, rather than to tell them to not do an action. In the brain, it's easier to process.
For instance, "do not do evil" registers in the mind to think about evil first, then try to avoid it if possible.
However, telling someone to "do good" registers in the mind to think about good first, and then think of ways to do it.
In children, telling them "don't sit down" will make them automatically think about sitting down, because that's what they heard. It's like telling someone "don't think about a purple hippo," they will think automatically think about a purple hippo. Instead, if you want a child to stand up, just tell them "stand up" instead of "don't sit down." It doesn't just work with children. People are better with direct requests, rather than indirect requests.
If you want to teach a child to do good, you have to show them. It's kind of like acting or miming class. If you want them to hug, you hug your own arms, and the child will see it visually and copy that action.
However, if you tell them to "stop" "don't do this" "you're bad" they start thinking that way, and behaving poorly, because that's all they ever hear.
Of course, being taught to "do good" and being taught to "not do evil", sounds like it would logically to result in the same thing, but in practice, the results would differ.
It depends on your definitions of both words. If goodness is merely the absence of evil, then "teaching good" and "teaching no evil" are identical. Is there such thing as a neutral act where neither evil nor good is done? If not, an act is either good or evil. Therefore it is essentially teaching exactly the same thing thus making neither "better".
If we only teach to not do bad, the net good to society will never be more than 0 (ignoring the possible accidental good), however, if we teach them to actually do good, there is the possibility that they could increase the good well above 0, even if there are accidental evil acts.
From a purely moral perspective, the honest response is to acknowledge the that ones obligations do not extend to charity. One is entitled only to what one is owns and is owed, and obligated to give only what is owed to, or owned by, another.
It will reinforce a sense of entitlement. Teaching a child to do good will, via omitting the previous fact, would not teach them that they themselves are not entitled to another's charity. This could lead to destructive behaviors towards those who do choose simply not to do evil.