In mammals and in most animal species, size affects metabolic rate. Metabolism is all the processes inside a creature that keep it alive. These processes are all the chemical reactions in and between cells. read more
This is why smaller mammals have faster heartbeats. Its also why cold blooded animals like reptiles have slower heartbeats than mammals. Their metabolism doesn’t need to run as fast because they don’t need to keep their blood warm. read more
So as for "why" I would argue that smaller animals have faster heart beats, and faster metabolic rates in general (see graph below), and this is the source of their shorter lifespans. As an allegory if you drive 100,000 miles on a car it will need maintenance, much more than if you drive 10,000 miles. read more
It is the same in humans as well. Babies and children have faster heartrates than adults do. It is because the stroke volume of little hearts are smaller than that of bigger hearts. Stroke volume is the amount of blood pumped each heart beat that is a formula of rate vs. strength of heart beat or contraction. read more