Why doesn't the negative feedback current in an op-amp inverting amplifier drive the op amp into saturation?
...( I imagine the current now is from Vin to Vout ) which means that the
V- will also increase...

OK, current does flow from Vin, through \$R_{in}\$, and then through \$R_F\$ to \$V_{out}\$, because for this opamp, &quot;+&quot;input and &quot;-&quot;input are assumed to consume no current. Right so far...
Why should V- increase?
When Vin is at a positive voltage, and Vout is at a negative voltage...somewhere in between there exists a zero voltage. Guess where this happens?...at the opamp's inverting input pin.
Opamp's inverting pin in this circuit must always sit near zero volts. We call this point a virtual ground, because it mimics the real ground on the opamp's non-inverting input. You might think of this virtual ground as the fulcrum on a see-saw: when one end goes up, the other end goes down.