Asphyxiation (suffocation) was originally suggested by doctors Hynek and LaBec, based on descriptions of torture by suspending an individual by their hand directly overhead, with their feet unsupported. This type of torture (called Anbinden) was used in the Autro-hungarian war.
Similar torture and death was used in the Nazi concentration camp at Dachau. Torture victims would struggle, appearing to be unable to breath. Deaths by this method are described as agonizing, where the victims appear to die by slow suffocation. This lead Hynek to believe the suffocation (asphyxia) was the most likely mechanism of Jesus’ death. Death by this type of torture would occur in about three hours, however.
The idea that Jesus died by asphyxiation the most widely accepted hypothesis of how Jesus died to the general public. There is no question that it would be more difficult to breath while hanging on a cross. Muscles arising from the shoulder girdle and attaching on the chest wall would create an extraction force to the chest. This could cause respiration to become paradoxical (reversed in mechanism). Exhaling would become an active process, requiring pulling up with the arms to allow the diaphragm and chest wall muscles to relax to let the air out, and inhaling becoming a passive process occurring when the arms relax, again causing an extraction force to the chest wall forcing air into the lungs. Presumably, on the cross one would have to pull up with the arms to allow expiration, and inspiration would become passive and occur when relaxing from pulling up with the arms. This is reverse to normal respiration from respiratory muscle activity.
However, if respiration depended exclusively on pulling up with the arms, fatigue and death would rapidly occur. But, crucifixion victims might remain on the cross several days before dying. Additionally, Anbinden is not analogous to hanging on the cross. During Anbinden, hands were tied overhead and the feet unsupported. In crucifixion, the arms were outstretched and the feet fastened in a stationary position. Crucifixion, even with Jesus, lasted much longer than death by the torture of Anbinden.
The Romans noticed that breaking the legs of crucified victims, crurifragium, hastened death. It may be that fracturing the legs during crucifixion caused a modified-Anbinden mechanism of death. Jesus legs were not fractured, however, since he had already been pronounced dead by the Roman Centurion.
While breathing would have been undeniably more difficult on the cross, suffocation as the primary mechanism of Jesus’ death seems unlikely.