I was born in 1940; my sister was born in 1948. Yet, it seems as if there is a generational gulf between us.
My values aren't much different than those of my parents -- born in the teens and survivors of the Great Depression. My mom, now 93, and I see things pretty much alike.
My sister's values, however, are those of the sixties -- liberal, permissive, "modern". We see eye-to-eye on virtually nothing -- politics, economics, child-rearing, cultural, you name it.
I can't imagine an athletic (or scholastic) competition where "everybody wins". Like you, I came from era when there was one winner and you learned from your losses.
My sister, on the other hand, believes that competition is "unhealthy". By her lights, there shouldn't be any losers. Unfortunately, that creates a circumstance where there can be no winners, either.
And when there can be no winners, why play...???