The real meaning of 狗 (left side only?) 犬 大 is no doubt lost forever to time. But from what I understand through 図説 漢字の成り立ち辞典 and elsewhere, these are a few of the viable theories : an opened mouthed dog that was waiting for his long overdo dish to be delivered/begging, a dog that watched over his owners plates and saucers....and for the evolution of characters, others of the more macabre variety centering on human sacrifice with the arms in a spread position 大, patterned after dog to god offerings perhaps)...