Government debt is different from personal debt. People don't work forever, or live forever. Buying a home on debt is a good choice for a person, since it lets them have a place to live after they stop working. And that debt is backed by the house: if the person dies before the house is paid off, they get the house rather than coming after the heirs for debts.
The government never retires, and never has to pay off its debts. That gives it a lot of leverage, but it also obligates new citizens to a share of the debt as soon as they're born. Your parents can't pass their mortgage debt to you, but they do pass on their share of money that the government has borrowed.
So the government can safely borrow money, but at some point it will accumulate so much debt that people begin to doubt its ability to pay it back. Whoever is left holding the bag at that point will be in very deep trouble.
I don't know what point that is. Interest rates are still low, so the answer appears to be "not today" (and "not imminently"). But the article points out that the low interest rates may be something of a false indicator.
So as you say, responsible debt is good. But decreasing revenue via tax cuts, and increasing debt accumulation, at a time when the economy appears to be booming doesn't appear to be responsible. It reduces the ability to borrow in the future, at precisely the time you could be increasing that ability by paying down old debts. Especially if you're then covering it up by borrowing in a way that's hard for people to see.