I'm going solo in a science fair even though my friends begged me to be on their team.
Why would you rather go solo over joining your friends?
Because I don't want to share the glory with others.
You shouldn't be so self-centered. Your friends clearly want to work with you as a team and you should help them out. Learning to share the glory of winning is an important part of life, and you shouldn't be so focused on hogging the spotlight.
I want to win just to shut my friends up.
Well it is your choice whether to join the team or be on your own. However doing it simply because you do not want to share the glory may not be a great reason. Either way, it is completely understandable to want to do things on your own at times!