Sins of omission kinda fall under the second category of what defines sin in some theology (I know it does at my church).
1-> Sins of commission: doing things that you know that you're not supposed to : basically doing the sin
2-> Sins of ommission: not doing things you know you should have done : basically neglecting to do the righteous act
Basically what your teacher is saying is that God has sinned by not doing things that He should have done... which is kinda funny because God is the One who decides what things should be done in the first place. So you can go back to your teacher and tell him that he committed a "sin of commission" in saying that God committed a "sin of ommission." God cannot sin, if He could, then He wouldn't be God. "Those who claim to have fellowship with the light yet walk in darkness are liars and decieve themselves." (1 John chapter 1 or 2 verse something) Don't forget that sin started by a serpent saying that God was wrong... and your teacher has done the same thing.