Because prices = money supply/goods and services.
I thought I'd pointed out the arithmetic blunder here before.
M⋅V = P⋅T
It is V, the Velocity of Money, that you overlook.
Which can be restated as
MV = PY
where Y is real output or GDP, as measured by all the (T) transactions in the economy - i.e. people providing each other with, and paying for, goods and services
And GDP = C + I + G + X-M
where G is govt spending (except transfers such as wefare payments). It's a
component of - not something
subtracted from - national income.
People struggle with this because they somehow think the same doctors treating the same patients - or the same teachers teaching the same pupils, etc - in the private sector adds to GDP, but is subtracted from GDP in the public sector. The common confusion of macroeconomics with a household budget.
If the govt net ("deficit") spends a billion dollars, both GDP and national debt increase by a billion dollars. Same debt to GDP ratio, bigger economy, all else being equal.
But all else is rarely equal since that spending effects the other components of GDP. That effect is called the
'fiscal multiplier'. Net govt spending might "crowd out" more efficient private sector use of real resorces and have a negative effect on the other components.
For a multiplier of 1, both GDP and national debt increase by the same amount. If the multiplier is <1, debt increases by more than GDP. If the multiplier is >1, GDP increases by more than national debt.
So it's an empirical question of whether multipliers are less than or greater than 1. It's a tricky to measure variable ...
unless you conduct a bold experiment like most OECD govts implementing austerity programmes, as they did in the 2010s.
And the results are in - multipliers from net govt spending are, contrary to previous supposition, generally >1.
Net - "deficit" - govt spending tends to crowd private sector economic activity and investment
in,
not out.
(appologies to anyone who's already spelled it out, but the thread is nearly 300 pages long).