Some people think that the clear sense of competition is more useful for children rather than co-operation skills, but others not. Such skills have advantages in some aspects that i'm going to discuss.
Firstly, advancing competitive skills in children, would be not only their advantage compared to other children, but also may be their skill issue in teamworking and comunicating with each other. It can also be good help to be independent among their mates and friends. Otherwise, competing with others, can also upgrade the productivity in their work, for example, they are working in any company, and somebody is better than him, but due to his competition skills, they can easily become the best everywhere. However, these actions in career may block or bother their teamwork ability, which can impact their reputation at work, in society and etc.
Secondly, co-operation with people in groups, can improve comunicative skills, which can help to get a job easily. Also working in groups would increase the efficiency of work, but it doesn't mean that if you are working in group will not require competitive skills or in other words demand knowledge, and in first situation the aspects remainig the same, if you are good at competing with others, it doesn't mean that you will not improve your comunication abilities. Consequently, these both skills are related to each other.
In conclusion, such abilities are are good in so many aspects, but if parents will teach their children how to connect these skills to each other, it would be more greater, than teaching only one of them.