Why Doesn't Win-Win Feel Like Winning?

Our first negotiation exercise for MBA631 was pretty simple. I was selling a biomedical manufacturing plant, she wanted to buy it. In the end, it turns out that McKensie and almost exactly split the difference between the next best case for each of us. $4M more than I could have gotten otherwise, $4M less than the most she could pay.

Perfect solution, right? Best of both worlds for both of us, right? No hard tactics, no manipulation, nobody was taken advantage of.

So, why am I still trying to convince myself?