“but the sin nature is transmitted through the man not the woman.”
Might I remind you that it was the woman who first ate of the fruit so it would more likely be stated that sin was passed from the woman to the man.
Eve was deceived. Adam was not. Adam was our representative through male headship. He was not deceived but willingly disobeyed God ... HE is the source of sin and death in the world.
Paul makes this clear.
dartuser is correct on this one.
The man genetically passes on sin.
This also explains the Virgin Birth. Why Christ Jesus not only was both God and man, but the only human since Adam who was eligible to become the Perfect Sacrifice.
The first sin was attributed to Adam because he knew he was acting wrong and acted on volition to disobey God by acting independently of Him.