What fallacy is this? It's not right for our government to pay off all student debts when I had to pay off all of mine.

Just seems like an opinion to me. Fallacies tend to arise when we ask someone why they believe something, and they use faulty reasoning.

EDIT: See my reply to the OP below. This could qualify as a fallacy after all.

I think what was really meant is "it's not fair" to treat the same case differently.
What those people criticize is the double standard in those situations. And that's not a fallacy. The world is indeed unfair and humans are not equally lucky.

So I think what was meant is "it's not fair for our government to pay off all student debts when I had to pay off all of mine". And it is unfair. That doesn't mean it shouldn't happen. When something non-beneficiary is happening, some people have been treated unfairly. Should we never change that because that way indeed they would have been treated worse than younger generations? That's equalizing downwards.

The question about what should be done (what "is right") is really a question about fairness or progress. It is indeed unfair to treat equal people unequally. But progress is always unfair to the previous generations. Continuing something because that's how it has always been, would be appeal to tradition .

This, among other things such as a faulty syllogism, is a false philanthropy. Using force to take from one to give to another does nobody any good. I suggest a review of the 1850 book by Frederic Bastiat entitled "The Law," especially the section on plunder. The entire book is only about 60 pages, and is available free.