What people are pushing back on is why all of a sudden is it a problem to deport criminals?

It's not.

It is a problem to deport people who are accused of being criminals (but that we don't know whether they are or not) without giving them an opportunity to contest whether they are criminals or whether they are subject to deportation.

It is a problem to argue that the Administration has the sole and unreviewable authority to declare that someone is a criminal and can be deported, even if that person has not been convicted of a crime or gone through the process for having an order of deportation issued.

That's not claiming it's a problem to deport criminals. It's claiming that it's a problem to deport people on the accusation that they're deportable criminals without the government being obligated to show that this is actually the case, if challenged. Or the government being required to comply with a court order that the people shouldn't be deported until the government makes that showing.

Albaby