no, it's not a false analogy at all.
The woman in this meme CAN comprehend forgiveness of sin- something so great as to send someone to eternal damnation but CANNOT comprehend forgiveness of something so much smaller than sin.
Student debt will not result in a 1 way ticket to Hell. Or even prison. Just crushing monthly payments that never end.
Which, frankly, it a lot like Hell.
And to the specifics of the word debt. The church I grew up in? When we recited the Lord's Prayer, we used the word debt.
Our Father, in heaven,
hallowed by thy name.
Thy kingdom come.
Thy will be done on earth as it is in heaven.
Give us this day our daily bread.
And forgive us our debts, as we also have forgiven our debtors.
See that word there? debt. As in a thing that is owed.
Even without that, the premise of Christianity is that faith in Jesus and following his commandments, will get you out of Hell. Because he forgave your sins. You no longer have to pay the price of eternal damnation.