That’s not too bad of an analogy. You did well. Most importantly, you are living out Christ in your life for your atheist friend to see. But for your final question: a guilty sinner cannot take the place of another sinner. It has to be someone who was blameless and not guilty of sin, who can substitute for us. That’s how I would explain simply what Jesus did.
FYI, there are plenty of similar sounding analogies about Jesus’ sacrifice. One I like particularly, that I learnt a long time ago from an evangelism seminar is the story about of the General of a guerilla army.
Because they were engaged in a guerrila warfare, they have to ration their food supplies to all the soldiers and civilians who were amongst them while hiding from their enemy. And to prevent anyone from stealing the food rations, the General decreed a punishment of a 100 public caning for anyone caught stealing.
One day, one of the guards of the food supply reported to him a good news. They have just caught a food thief red-handed in the warehouse. This thief has been responsible for the missing rations of a few weeks.
“Good,” says the General, “Prepare for the public punishment the very next morning, and everyone’s attendance is compulsory.”
But the bad news is the thief is his senile and sickly grandmother, who is also very very old of age. This troubles the General for the whole night.
The very next morning, everyone was gathered, and they argued among themselves. If the general were to punish his own frail grandmother, then he is not loving, and a heartless person who is not worth their loyalty. Another argues that if he doesn’t punish his own grandmother then he is not a just and fair man, one they cannot continue to follow.
But at the General’s order, the punishment will still take place, and he walked towards his grandmother and freed her and took off his own shirt and robe, and ordered the guards to lash his bare back instead.
Somehow this story stuck with me and it has been mighty useful so far. Would love to hear other analogies to best explain Jesus’ sacrifice.
Hope it helps, blessings.