For purely informational purposes - the human vocal cords will not function unless air is passed over them. In other words, if you are not breathing the vocal cords will make no sound. Also, if you are saying "I can't breath", you are, in fact, breathing. Now, when pressure is applied to your throat it is very uncomfortable, but if you can speak, you can breath.
Buzzzzzzzzzz, Wrong.
The lungs have what are called "Volumes" and "Capacities". For our purposes, you need to understand these two phrases: Functional Reserve Capacity (the amount of air left in the lungs after a normal exhalation) and Expiratory Reserve Volume (the amount of air you can still force out of your lungs after a normal exhalation).
When you take a normal breath you breathe in and out you are breathing about 500ml of air. After breathing out, you are left with ~2400ml of air inside your lungs, this is the Functional Reserve Capacity. If you try to force out as much air as possible, you can still force out ~1200ml more air. This is the Expiratory Reserve Volume. This is air you are able to speak with even if you cannot take a normal breath. Important Note: Notice that the Expiratory Reserve Volume is more than twice the size of a normal breath. That is a lot of air you are able to force out, and a lot of speaking you can do even if you can't breathe.
The lungs work on negative pressure. So, your lungs, when you breathe in, are at a lower pressure than the outside air. This draws the air into them. This is caused by your diaphragm and intercostal muscles. Your lungs are very elastic, and will move back to their normal size during exhalation. This is where the problem begins for officers. If you are kneeling on a suspect, or you have them handcuffed on the ground so that they are on their chest, there is a strong possibility that you can cut off their ability to breathe. Once the lungs begin to exhale, they collapse, but if you they are being pressed down on by body weight, they may not be able to re-expand. They then continue to collapse, forcing out the Functional Reserve Capacity of air, but not drawing in a new breath. So, your suspect may be pleading for breath, they may actually be incapable of drawing one in, and the reason is you. If someone is saying they cannot breathe, you need to believe them, because you might be killing them. Furthermore, during any kind of physical altercation, that person may be breathing deeply and rapidly, making their lungs collapse faster when you are kneeling on them or holding them on the ground.
Asthma. Some of you may be saying "Well, the guy who died in LAPD's care had asthma, that wasn't the officer's fault or the jail's fault." Oh yes it was. If someone is telling you they have asthma and they can't breathe, you need to believe them. Asthma is a constriction of the airways, no different than being strangled. They will still be able to speak and they will still be dying slowly. It took 30 minutes for that man to die, and that was entirely preventable.