I think it was a lose lose situation. Had he dropped it right away, no drama.. either the kid was trying to stall in order to try and get an advantage to shoot them, or he was holding on for no damn reason other than to get shot. Since it was a kid who probaby wasn't a hardened killer, it makes more sense that he would drop it, especially if Carl had the drop on him anyway. Another example of how the shows director made it a sloppy situation.
While I think Carl certainly has issues, in this instance, it's hard to get too upset with him shooting. The guy hesitated, held on to the gun when told to drop it even though he was going through the process of attempting to drop it ( it must have been super glued to his hand and he was too embarrassed to say it) he wasn't dropping it. The guy did come to the prison to kill them after all