If you think that's tough to do, try convincing someone that a tactical scope with 1 MOA elevation and 1/2 MOA windage is just as precise as a 1/4 MOA scope. Again, it boils down to nobody can hold that close. Up close, 100, maybe 200 yds., yes. Try it at 500-800 yds.
I think you explained it fine. He's just got his mind made up that a 1/8 MOA scope has an edge. He needs to try it himself. E