Pro: 1) it improves the net worth of many households; 2) cancelling the debt would improve their ability to get mortgages and other debt; 3) most student debt is held by the Federal Government anyway and even if cancellig this debt affects the government's balance sheet, it's a lot easier than if it were held privately.
Con: 1) It does nothing to improve the cost of higher education going forward (like tuition levels, administrative costs, funding for research, salaries, pensions etc.), not does it prevent for future students from contracting student loans and accumulating student debt (it's not a reform of how to finance a college or postgraduate education, another debt forgiveness will be called for in a few decades); 2) a lot of student debt is owed by households in the upper half of the income distribution, which makes sense for many reasons, such as very poor people don't have student debt because they never went to college, or people with advanced degrees (masters degress, medical degrees, law degrees, doctoral degrees, etc.) tend to be higher in the income distribution and also accumulate more student debt; 3) payments of a lot of student debt programs depend on income, so the higher earners with student debt make most of the payments; 3) some student debt is held by private companies, so to cancel that debt, the Federal Government would have to purchase it first. (although it wouldn't be such a big expenditure at a fair price for it).
But, students with very wealthy parents can go to college without getting into much debt, so there's that. Overall, I think that free public four year colleges would be a better policy going forward, and much more progressive (in the sense that it benefits people in the lower end of the income distribution than in the upper end) than debt forgiveness. And you could combine that with means-tested debt forgiveness.
Final note: the 2010s were a decade of very low inflation, and that is also a factor in the burden of any debt.
