Why would I be arrested for manslaughter in this instance?

OKAY! So you saved the dog, which meant that in that instance, it was within your capacity to save the baby, but through inaction, negligence, or disregard for human life, the baby died. On 9/11, the buildings collapsed and were burning, and it was not within any one person's capacity to save the people in the building, since there was dust which would be hazardous, collapsing rubble, and the jet fuel fires. This was a bad comparison. But you had a choice to save the baby and you didn't, therefore you commited a murder through inaction, etc.