Some people in this world want to try their hand at everything. Rather like a bee that flies from flower to flower, Others became intensely focused on a particular activity. These traits produce the generalist and the specialist. The world needs both. The fellow who spends his life developing green dyes will probably never run a company. That would be the job of the person with more divers knowledge.
Doesn't quite make sense. You say she "does not want to be good at anything." and then you say, "only to get very good and then she decides she does not want to do it anymore."
Sounds more like she does not stick to things rather then does not get good. I think at this age that sticking to something is due more to the socialization process and the instructor. Its normal for kids to trial and error things. Its good that she is trying different things. Either she will find an instructor that she likes and stick with it, or a bunch of her friends will also be involved and she will stick with that.
I would assume that you guys supported her gym activities by going and watching her perform? Or was she just dropped off and picked back up again? by the way - has she tried soccer yet?