My seven-year-old daughter doesn't want to try any type of sport or game. She says she doesn't want people to watch her. I believe that she's afraid she won't be good at it and is afraid of being embarrassed by losing or not being the best. Is this a self-esteem issue?
You have put a lot of thought into what is going on with your daughter, and it sounds like you are on the right track. Your daughter may be comfortable in trying individual sports with you. Perhaps you could teach her to play tennis (or take lessons together) or shoot baskets with you. The individual sport would take away the pressure of appearance in front of teammates, and you would be a non-threatening playmate.
Soccer is a great group sports activity for children your daughter's age. Not a lot of skill is required at that level, and all of the children enjoy running after the ball and trying to kick it.
There may be other groups which are not sports-related in which you could involve your daughter. Joining a Brownie troop or a church group may allow your daughter to become more comfortable in a group setting. She could gradually move into sports and game activities as her comfort level increases.