why does the year and a day rule existed at common law?

Answer 1

One aspect (element) required for almost any crime or tort is causation -- that the prohibited actions were the actual and foreseeable cause of the resulting harm.

In olden days, especially when medical knowledge was much more primitive, it was often difficult to determine why someone died -- and whether the death was a result of the harm caused, or was due to some other independent cause.

So they came up with a simple rule -- if the death occurred more than a year after the attack/injury, then it could not have been caused by the injury. While that's not medically true, it was the best they could do at the time.