The US were playing an effective and very ugly 6-2-2 / 5-3-2 in the first half. It was this same style that saw them beat Spain in the semi. They relied on the aerial strength of their defense and inch perfect tackling. I heard people compare them to Greece in 2004, it is not quite true, but the idea was the same. Any errors in their tackling would led to cards, which we saw in their group matches. For offense they rely on set pieces and the counter attack. Against Spain their counter attack looked more like a dump and chase, in the first half of the final they had a more organised counter attack going and it paid dividends. The US had 2 goals in the first half and their defense held the Brasilians to the outside. The US style gifted possession to the Brasilians, and though they were passing much better than the Spanish they didn't cause too many problems for the US.
Which leads me to the title of the post, I don't know why they did it and I hope to hear some explanation from Bob Bradley. They came out for the second half and seemed to have switched from their hybrid 6-2-2/5-3-2 to a 3-3-2-2. This gave the Brasilians a lot more space which they exploited. The US counter attack that had been organised in the first half became the more desperate dump and chase that they resorted to against Spain. The only advantage that this system seemed to afford the Americans was more of the ball if they managed to hold it up in the Brasilian half.
The only thing I can think of is that Bradley thought that switching formations would allow the US to have more of the ball and thus limit Brasil's chances. Implicit with this way of thinking is that the US was good enough to play against Brasil. This is nothing other than overconfidence in the fact that they were up 2-0, or perhaps they believed all of the hype that they had no doubt heard about themselves from the excited US media. Whatever the reason it was a stupid decision. The US looked lost for the entirety of the second half. Compounding the problem was that it only took Brasil one minute to get a goal in the second half. Brasil kept on coming and got a second through Kaka only the ref didn't notice that the ball had crossed the line (and didn't count it). A quick aside here is that on disputed goals the ref should blow their whistle the fourth official watches the replay on a TV and provides the correct decision. As you are no doubt aware Brasil kept coming and won the match 3-2. The US offered no resistance in the second half.
I believe that if the US had stuck with their ugly football through the 6-2-2, they may have won in regulation or forced extra time. The players on the US are not as good as the players on Brasil, but with the formation they started the game with they could have won. Why they changed their formation confounds me. The whole purpose of starting with a formation like the one the US played was to hold out for a draw or possibly grab a goal on the counter attack. So to be up 2-0 would have exceeded their hopes. I am not sure what they discussed at the half, but as far as I can tell they got overconfident and thought they could play the Brasilians. They couldn't and they lost.
In any tournament there is always a lot of talk about teams getting overconfident and looking past opponents. Surprisingly in the final the team that fell guilty to overconfidence was the under dog. They changed their formation and in the process threw away the title, that has got to sting.