If you mean "physically print" money, you're technically right. In some countries.
But I think in this discussion, most of us are thinking about "virtually printing" money. That is, creating numbers in your bank account.
Again, you're technically right in that the government is the one steering this process. But the practical matter of actually "printing" the money is handled by the banks. It's their decision when and where to "print" money, as long as they have enough reserves at the end of the day.
Well pretty much everything is regulated by the government but banks still create money.
As for reserves, have you, or anyone you know with a good credit record, ever applied for a loan and gotten told, "We would like to lend you money, but we are all out of money to lend due to reserve requirements. Can you check back in next week?"
That doesn't happen. The bank creates the money and deals with reserve requirements later.
Banks don't print money. The government can.