First of all, there was an agreement between the creditor and the debtor about how the money would be repaid. The balance sheet cannot be wiped clean. Someone must pay the debt or creditors will stop lending money to students. I do not want the government to pay the debt. They spend too much money already. It's unfair to take tax dollars from someone who did not have a child go to college or who had one go on full ride scholarships and make that person pay for an unknown beneficiary of the government.
Next, from an efficiency standpoint, it doesn't make sense to give money to college graduates. They are going to have higher earning potentials than the less educated of their cohort. Forgiving $50,000 in student loans for an individual might lower their monthly obligations by a couple hundred dollars, but will they spend all of that? If you gave that same money to 50 poor people in the sum of $1,000 each, the poor would spend that money a lot faster and probably on more "needed" stuff than the former students.