Why is this amplifier inverting that voltage?
Try using negative feedback and not positive feedback. The circuit you have shown is nonesense unless you are trying to make a comparator with rather a lot of hysteresis.

When using a simulator it might theoretically "settle" on what seems to be an improbable scenario - If the output is -1V and the input is +1V then the voltage at the non-inverting input is 0V and this exactly matches the 0V at the inverting input. 

Ergo, what seems to be a stable situation.

For a real circuit this just would not happen - a tiny bit of noise or drift would polarize the situation and the output would be hard against the positive rail.