How does a person dying on a cross save me or take away my sins?
Because it was the ultimate sacrifice, the Son of God, expressly offered up to God for your sins. It was the ultimate, perfect act of worship. No other comes close.
One way to think of it is as a gift Jesus gave to The Father. The ultimate gift, the ultimate act of love, the most valuable thing any of us possess, made all the more valuable because of who Jesus was.
On a more mechanical level, Jesus had to submit to the evil torture and death in order to conquer death and evil. He could not have conquered those by avoiding them just as an army on a battlefield doesn't conquer by avoidance. Conquest is done by engagement.
There have been volumes written about this, so please forgive my humble & incomplete explanation. I suggest you research this further, always keeping in mind God's infinite love for each of us.
https://www.catholicstop.com/archiv...s-instead-of-just-saying-youre-forgiven/
