It's all about competition and challenge. And skill growth, improvement.
For pure furballers that equates to 1 v. 1 dogfights. The individual against the individual. No more, no less.
For the Win-The-War types (WTW), it's about team vs. team, whether that team is your wingman, your mission, squad, or your country.
The enemy has challenged you by attacking your base, so you defend, individually if you prefer, or collectively. For the furballer, it's an even simpler challenge in that the opponent has taken up an airplane into YOUR air space, effectively challenging your ACM skill. So you accept that challenge and compete to win, 1 v. 1.
For WTW people, there is more to the game available to them than that. The enemy simply has bases that should be yours, or attacks your bases, or simply exists as your designated (by the game itself) as your opponent - that's the challenge. The competition (in AH) is to protect your bases and take his, but collectively, using teamwork, tacticals and cooperation as well as using ACM skills when flying. It is so much a greater skill challenge than just being a hot ACM dogfighter. But to each their own.
I like furballing now and again, and try to get better at it, but it becomes very pointless and boring for me if that's all there is to this game. For some furballers, that's all there needs to be. There happy with that, and that's fine.
For me and other WTW pilots, having a game structure that focuses attention on more than just 1 v. 1 (but including that from time to time) is essential to continue to enjoy the game over time. That and the fact we enjoy the teamwork aspect -- the cooperation and skills needed to acheive concerted joint effort -- the goal of which is to take bases. This gives the dogfighting aspect more purpose, meaning it stays enjoyable longer.
And for some, there is the historical simulation aspect. The enjoyment of pretending what it was like to fly in a squad in combat during WWII (or as close as we can expect here). That adds another dimension and level of enjoyment for many that they wouldn't get by just furballing all the time.
We all really want the same things, competition, a challenge, a chance to learn and display our skills. One just has a more limited focus as a furballer, and a broader one as a War Winner.