I believe that healthy competition is good, but being competitive over every single thing in life is not healthy. I regularly encourage my children to race one another when we are outside playing. The running is healthy for them. My 2 and 3 year old girls don't care about winning. They are happy to just be running with their brothers. My 4 year old son and 5 year old son tend to be more competitive. My older boy runs faster and my younger boy tends to get upset that he never wins. A part of parenting is teaching children sportsmanship. Learning to lose and have fun doing it is a part of that.
We also participate in activities where my 4 year old surpasses my 5 year old. This is a healthy type of competitiveness, and in the process they both learn to win and lose gracefully.
I do not believe that I will ever encourage, or even condone, a competitive nature when it comes to anything that is academic. Each child is extremely different in the way that they learn and in what topic interest them. I feel that any competitiveness here would just hinder the children from reaching their full potential in those topics that they are less adept in.
Overall, sibling rivalry is great when it is fostered in a healthy way and not allowed to get out of hand. Competition between siblings is healthy just as competition between children in a physical education is healthy. However, it is not healthy to allow the children to turn everything into a competition, and it is not healthy for their adult role models to try and get them to compete over every aspect of life. This is how children are led to believe that those who provide their care will only love the one who wins.