It is true that there seems to be a correlation between lifespan and metabolism, and generally larger animals have lower metabolism. But you have to consider animals of separate groups separately because ectotherms like turtles have very slow metabolisms compared with endotherms of similar sizes. Also, birds have very high metabolisms, but live surprisingly long lives.
So it’s best to compare mammals separately, and you certainly do see a correlation. For our metabolism and size, humans are big outliers. We live much longer than you would expect. So it’s not so much why big cats have short lifespans as much as it is why humans have such long lifespans.
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