Another way to look at it is this. Let's say cycling isn't a factor. For some reason you can play an Ambassador every single turn, and your opponent can too. If you use the Ambassador to get rid of one card and give out one card, and then your opponent does the same, then you'll never win or lose that war. Because you'll just be trading cards back and forth.
However, if, while your opponent is getting rid of one and giving out one every turn, you are getting rid of TWO and giving out one every turn, eventually you will have a slim, non-junked-up deck, while your opponent is merely breaking even. You'll win the war and can then start buying powerful engine pieces or whatever is required to get rolling.
If you both get rid of two and give out one every turn, the Ambassador war still ends in a tie, but it does end, eventually, as you'll both wind up with lean decks.
What I'm getting at is that, assuming you can play your Ambassador with equal frequency as your opponent, you can't win an Ambassador war by only getting rid of one card every turn. You can only tie at best or lose it.
The reality, of course, is that you can't play Ambassador reliably every turn. You can't even guarantee you can play it as often as your opponent can, because things like missing the shuffle and Amb/Amb collisions can decrease your ability to play it. Those problems are out of your control, but you can control other things that would tend to increase the frequency with which you can play it, and that's deck size. Decrease your deck size, and you will tend to be able to play it more often. How might you do that? Returning two cards instead of one with Ambassador should do it!
In other words, returning two cards instead of one helps you along two separate dimensions, resulting in an exponential advantage to yourself: you double the progress you make toward winning the junking war, and you increase the frequency with which you may launch those junking attacks.
