In short, it is measured in your breath because your blood is oxygenated in your lungs. They have you make those long, deep breaths to draw from deep in your lungs. The device is quite accurate.
You can always refuse a breath test and opt for a blood draw if you choose... but that ensures that you will be arrested.
Just a note. The law says you have the right to examine evidence against you. There is no way to examine a breath test. Just something you might discuss with your Lawyer