How can a government print more money than it takes through taxes and borrowing? Why would a government do this

First of all, the federal government doesn't create money; that's one of the jobs of the Federal Reserve, the nation's central bank.The Fed tries to influence the supply of money in the economy to promote noninflationary growth. Unless there is an increase in economic activity commensurate with the amount of money that is created, printing money to pay off the debt would make inflation worse.