The scourging came before the sacrificing. Not to mention
Leviticus 17
11 For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.
The Gospels indicate Jesus' blood was not shed to a degree that would make blood loss from the body the exclusive cause of death. Death solely by blood loss is the only biblical cause acceptable for an animal's sacrificial death.
casuistry
Noun
reasoning that is misleading or oversubtle [Latin casus case]