(expanding on what other posters have already said)
Cash is a liability of the central bank, yep. Destroying it removes a liability from the bank's balance sheet, increasing their equity. As others have noted, destroying cash is equivalent to returning money to an arm of government.
As you say, if people destroyed cash on a regular basis, it would be deflationary: the central bank would respond by lowering interest rates. When the increased equity was eventually booked as profit, it would go back to the government, who would (presumably) spend it.
Both the lower rates and the increased spending are inflationary, so in the long run we might expect that the system would balance itself out.
Cash is a liability of the central bank, yep. Destroying it removes a liability from the bank's balance sheet, increasing their equity. As others have noted, destroying cash is equivalent to returning money to an arm of government.
As you say, if people destroyed cash on a regular basis, it would be deflationary: the central bank would respond by lowering interest rates. When the increased equity was eventually booked as profit, it would go back to the government, who would (presumably) spend it.
Both the lower rates and the increased spending are inflationary, so in the long run we might expect that the system would balance itself out.