Why do hummingbirds have such high metabolic rates?

One reason hummingbirds have such high metabolic rates is because they are so small. It hinges on the relationship between body size and surface area. As the size of an animal increases its relative surface area becomes smaller. And as animals become smaller their relative surface area gets

Two equally warm cubeys. Which needs to eat relatively more?

larger. If this is not intuitive, imagine two animals shaped like cubes. Call them "cubeys." Look at the small cubey on the left and compare it to the larger cubey. The larger cubey is twice as big, if you measure bigness as height or length. Notice how many cubes make up the larger cubey. There are 8 of them. Also notice that only 3 of the faces of the little cubes in the larger cubey are exposed to the external surface, but 6 faces are exposed in the smaller cubey. This means that the smaller cubey loses heat twice as fast as the larger cubey because it has relatively more surface area for its size than the larger cubey. The same holds true for real animals. Their shapes may be different but the relationship between surface area and volume (weight) holds true: larger animals have relatively less surface area than smaller one. 

This means that a small, warm-blooded animal will have to generate more heat per unit of time than a larger, warm-blooded animal. To do this it will have to eat relatively more for its size than the larger animal. Thus the hummingbird consumes more than its weight of nectar in a day while we get by with just a small fraction of our body weight. Notice that it is relative amounts that are involved. The hummingbird only weighs 2.5 grams, but consumes 3 or more  grams of nectar per day. We obviously eat more in absolute weight per day, but far, far less than a hummingbird relative to our body weight. 

This surface area/body size relationship also explains why you need to bundle up your babies and small children even when the weather is mild. A tiny infant or child will chill much faster than an adult because it loses heat more rapidly in relation to its body size than an adult would.