Lowering taxes only theoretically reduces the amount government will take from people who lawfully earned it and then spend it. It does not take money away from anybody who gainfully earned that money and give it to somebody else.
Letting one person off the hook so that the tax payer then has to pony up the cash to pay a debt is something quite different. The government guarantees the loan rather than provide them so if the government forgives the debt, somebody in the private sector will take the hit or the taxpayer will.
It's like me telling you that you are not obligated to pay off your car loan and the credit union will just have to eat what they are owed. Or those other people will have to pay it for you.
If the government provides the student loans direct from the public treasury it is the same thing. So long as there are strict guidelines for number of hours taken, passing grades, etc. in order to get or defer a loan, and enforced rules for repayment of the loans, that is more acceptable to me than a lot of government programs. But if the government then forgives the loan, that comes directly out of my pocket and I resent that a lot.
But, what Obama did is not really forgiving their loans. Yes, he has reduced their payments based on a percentage of their discretionary income, but their interest still accrues and they are still responsible for that and the principle. After a pretty long time, yeah, their loans are forgiven, but after that time period, the likelihood of them ever paying is probably zero. And, if they are already in default, I would hope that their wages are garnished as happens with all other federal government debts.
Out of principle - personal responsibility - I am against it. I would love to have the same payment plan for my debts.
Pragmatically, it makes sense. However, as I have little trust for this administration, I am not sure that he will actually fully forgive these in a few months. He appeases the adoration masses with what appears to be forgiveness and desensitizes the opposition with non-forgiveness, then moves on from there. Only the observant notice at that point.