I can think of a good reason why Rodriguez would not want to leave a loaded gun in his apartment while two drunk people were fighting.
I can think of a good reason why it is not a good idea to sneak up on a military veteran who has served in Iraq, although the cops didn't know that at the time.
Rodriguez was waiting for the police to arrive, and he probably expected them to drive up to his apartment with lights flashing, rather than coming at him from behind the apartment. If they had driven up with their lights flashing, he probably would have put his gun down. Since he wasn't aware the cops were there, it was logical for him to still be holding his gun.