Sinning, as Jesus and the church say, is good. Turn or burn Christians.

[Greatest I am]

There you have it. If you can see good and evil in cooperation, then your previous statement -when we cooperate, there is no harm, lose, sin or evil-
cannot be true.  It is not an issue of logical and reasoned fact.  

Sin, otoh, is present whether we do good or evil.  It's the x that makes us contemplate wrong behavior or engage in wrong thought even as we do the right thing, and even if we never act on it.  I don't agree with your ideas about cooperation and competition as good and bad making properties - but the beauty of sin as a concept is that it's metric neutral.  Sin is not competition...sin would be the thing that compels you to compete when you could cooperate.  Sin is the x that makes it difficult for you to see opportunities to cooperate.

??

What harm did I show in cooperation? 

I did show harm to the opposing group but the internal cooperation of the first group is good for all within it.

For the out group, sure, they will see evil in the others cooperation while giving full marks to his own side's cooperation.

I do not deny that in our dualistic universe, cooperation likely has the evil side of not finding the fittest in the one side, or both, but like in the WWII scenario, there was a greater good at stake and our cooperation saved us from speaking German.

"Sin, otoh, is present whether we do good or evil."

I take it you mean a thought sin, and disagree, as scenarios can be thought up as comparisons without the thought of personally doing the act.

If that was not your point, show an example of what you mean.

"Sin is the x that makes it difficult for you to see opportunities to cooperate."

Our selfish gene is what leads us. It defaults to cooperation in us when young, as that is the best survival strategy. 

Later, when we start to compete is when sins would come to mind. We wish to win and will do what is acceptable, generally, to win.

Regards
DL