In the old gold standard post war economy you would be correct. If the currency were finite, or inflationary if multiplied, any distribution from government would amount to someone else losing some measure of currency or its value.
However, we are no longer constrained by such archaic standards and the government is the sole issuer of currency that also denominates the debt. This means that currency can be injected into the economy without devaluing existing currency, or having to collect (taxes) from anyone else first. Our debt is now an almost meaningless number, in spite of politicians using it to beat us about the head and shoulders should we suggest that we would like nice things like other nations have. In fact, the only reason we still measure such things as debt is to set bond prices and give wealthy people and banks welfare.
We left the gold standard in ’71, but the institutions of finance went on as if nothing changed because they profit from the old system. The truth is that taxes don’t fund government spending and aren’t even absolutely necessary, so no one is being “robbed” when government finances programs for the poor. This was always mostly true anyway as wealth accumulation is extremely dependent upon a healthy society and economy. You libertarian types should all be given an ax and some land and told to go make your first million without the benefit of infrastructure or “our” money.