The V+ and V- inputs are not forced to be zero by the operational amplifier. The voltage between the V+ and V- inputs are forced to be zero by the interaction between the output and the passive components that form the feedback loop. Without any feedback components here is the equation of an Op Amp:
Vout = A(V+ - V-)
Vout is limited by the source voltages Vs+ and Vs-:
Vs- < Vout < Vs+
Please notice that A is the open loop gain of the amplifier, which is always very large; 100,000 to 1,000,000 is a typical range.
So what happens, if V+ - V- = 0.001 and A = 100,000? The output is going to try to go to 100 V but Vs+ is usually 12 V to 15 V. From this we conclude that an Op Amp is meant to be used with passive components that provide feedback that gives the amplifier its stability with predictable characteristics.
Lets consider the Non-inverting amplifier:
V+ = 0
If the output was anything other than 0, it will move toward 0, which forces the voltage across R2 to approach 0 and the same for the voltage across R1. Therefore, forcing V+ to be 0 cause Vout to be 0 which forces V- to be 0.
Let's make V+ = 1 V. The gain of the amplifier causes Vout to raise to decrease the difference between V+ and V-, in accordance the resistor divider equation V- = {R1/(R1 + R2)}Vout, until the difference is 0.
Let's look at the inverting amplifier
V+ = 0
If Vin = 0, Vout moves toward 0 so that the voltage across Rf = 0 which makes voltage across Rin = 0 and V- = 0.
If Vin becomes 1, Vout moves in a negative direction so that V- becomes 0 in accordance with the equation Vout/Vin = Rf/Rin