OP Amp output voltage half
Congratulations on being keen enough t0 learn by experimenting!

The LM358 / LM324 have an input common mode range of Vcc+ - 1.5V.
This means Vin on either input needs to be 1.5V or more below Your V+ supply.
This is specified in the data sheet.  

In this case V+ is 2.4V wrt ground.
2.4 V - 1.5 V = 0.9V wrt ground.
This is the highest that either input can be at without violating the Vcn constraint.
Your Vin of 1.2V exceeds this :-(. 

Easier on the brain MAY be to start by operating the amplifier as a single supply amplifier with Vcc+ = 4.8V (5v?) and Vcc- = ground.
Then try a non inverting amplifier 


Input to In+,   
Rf1 from out to In- and   
Rf2 from in - to ground.
Gain = (Rf1+Rf2)/Rf2.     


This makes all signal referenced to ground (Vcc-) and stays away from the Vcm_max limit initially.

Then try inverting amplifiers (as per your example) by biasing In+ above ground by say 1V with a resistive divider.