Just because YOU lose half your income to taxes and inflation doesn't mean that income disappears.

Your taxes get spent by other people, is all. Taxes don't cause inflation.

Inflation itself continues wearing away the value of the dollar as more dollars are produced; those dollars are borrowed and spent by the government. THEY get the new dollars, not you. THAT's inflation of the money supply, which would occur even if the Fed was handing you bundles of cash directly. You're not the one getting the cash, though, making it even worse.