I think it's because there isn't really a thing called 'hard values'. Self-discipline is hard but it is also a 'soft value' - that is, a non-technical one, such as something related specifically to the sport.

I think others have covered the reasons why ‘soft values’ is the intended answer. I want to add that this passage is an inaccurate summary of youth sports in the US, in case you’re interested. Schools themselves are universal and offer physical education at all ages. That is rather limited, however, and does not include participation in team sports. For that, there are youth leagues, which are optional and usually not directly connected with schools. They are typically organized by volunteers and the youth players are characterized as ‘participants’, not ‘pupils’. At younger ages, they are focused on teaching how to play the sport and the teaching of ‘soft values’ is also important. As the children age, leagues can become more competitive and participation declines significantly. Middle schools and high schools offer teams alongside the youth leagues. Depending on the sport there are varying levels of competitiveness for these school sports and certainly for some sports they have their own culture, as the passage mentions. But ‘soft values’ are still a focus. The big difference is that the number of participants is much lower than at younger ages.

I think it’s because all kids take part and learn soft values, whereas fewer take part competitively where they learn hard values.

It's because in passage four, the sentence says; The 'athletic fields become LESS a place to learn about soft values'. The 'less' is the important word here. This means 'hard self-discipline' (a hard value) is learned MORE (or mainly) on the playing fields.

Yes, the sports field is 'mainly' about learning soft skills like teamwork and participation, even though it says later on this is less of a focus.