That's funny - underhanded chins eliminate arms? Doesn't make much sense considering it puts more emphasis on your biceps during the movement. That's why you can move more load in this instance, because the arms are in a more favorable position. If anything, wide grip, overhanded chins are the movement that would eliminate arms (and also limit the load you can use substantially) Or have you never tried doing them either that way?
If you are doing the right compounds, you won't need very much arm work at all for them to grow. For instance, chins, as already mentioned, hit the arms well, as do deadlifts, bench, bentover rows and military press, unless you are doing some weird version of each lift where you use legs somehow instead of arms to push and pull the weight bar.
In fact, I am of the opinion that you don't need to do direct arm work at all, except if you want to focus on arms during a cycle. The only arm work I do is as metabolic work during the 5s and post-5s.
But I don't have 21 inch arms, so what do I know?