I totally understand where you're coming from but there's another level of things too.
Older fans will remember far more about special City 'moments' in their lives far more than the wins and losses (barring the very significant ones). Their first City shirt, first match, listening to us playing in Europe on the radio etc. Winning the FA cup or the League are truly fantastic moments, definitely, but they are massively outweighed by the rich and fond memories of being a supporter than go well beyond the final score. You'd be hard pressed to find a more dramatic individual moment than the Aguero one, but over the lifetime of supporting City it will still never measure up to all the other memories combined, most of which weren't about end results.
At the risk of sounding like a hippy peace maker, I think you're both right, but at two different levels. The player changes we make are all about being the best team we can be in order to win. That's what a sporting team does, that's it's goal (pardon the pun).
But 'sport' magically offers more than that, and the drama for good and bad, and some of the memories I've mentioned above combine to make being a fan far FAR more than the end result. Otherwise, why watch at all? might as well just await the final score on a teleprinter right?
You're right that the feeling of winning is good, and the feeling of losing is not, and yet so many fans will endure the feeling of losing far more often just for the rare time they win. That defies the simple logic of it only being about winning - because if you lose more than you win, it's a net deficit. We go because we still enjoy the feeling of hope. That 'next time we might win!'.
So really, it's not all about the actual winning. It's the hope of winning, the dream of winning, and even sometimes, the 'we almost did it' moments or the plain old sentimentality of 'remember when...' and the result is almost an irrelevance when we look backwards at it.
