Can't balance differential amplifier circuit
The LM358 (like other op-amps in that similar range) has the ability to pull-down its output to close to 0 volts because it uses a 50 uA current sink on the output. Without that current sink, the minimum output voltage would be about 0.6 volts above the negative rail (0 volts in your example): -



And here comes the problem; your feedback resistor is acting like a pull-up resistor to 2.5 volts (set by R2 and Rg) and this negates the effectiveness of the internal 50 uA current sink because Rf will try and inject 250 uA into the output pin thus lifting it up above 0 volts.