I think the confusion here is due to the semantic ambiguity of "competitiveness".

A tournament can be called competitive and a participant can be called competitive, but these don't mean quite the same thing.

Evolution is inherently competitive, but humans become competitive by evolution.

>Isn't competitiveness at the core of biological evolution and not something we have "evolved to"?

In short? No. Fitness is.

I don't understand the distinction. Competition is at the core of biological evolution and so we, like all living creatures, have evolved to be competitive.

Many living creatures have evolved to be co-operative (including humans). Some (like humans) are often individually competitive within a larger co-operative social system. Others (like ants, bees, mole rats, some shrimps, etc.) are individually altruistic and collectively eusocial or hypersocial. Evolution is competitive at a systematic, somewhat abstract level: traits that promote perpetuation of themselves given the environmental constrains tend to prosper, and if the pool of resources is limited, the prospering of some traits will probably be detrimental to the prospering of others.

The distinction is between competition in the sense of individuals or groups competing, over things that are often irrelevant with respect to evolution, vs the fundamental principle that given a set of environmental constraints and a limited pool of resources, an entity that can repeatedly propagate more effectively than others will tend towards a greater relative abundance.

The fact that many extremely successful species are not individually competitive proves that evolution does not require all winners to be individually competitive.

competition is not at the core of evolution, survival is. competition emerges when the survival of one requires another not to survive. is that relatively rare or commonplace? i think it's rare but it's down to ideology.