Why couldn't Holden hit Stradlater with his left hand ?

From the text:

All I know is I got up from the bed, like I was going down to the can or something, and then I tried to sock him, with all my might, right smack in the toothbrush, so it would split his goddam throat open. Only, I missed. I didn't connect. All I did was sort of get him on the side of the head or something. It probably hurt him a little bit, but not as much as I wanted. It probably would've hurt him a lot, but I did it with my right hand, and I can't make a good fist with that hand. On account of that injury I told you about.