ANSWER: Because the cat has a combination of fast-acting muscles and a specialized skeleton. The cat's muscles consist mainly of "fast-twitch fatiguing" cells. They work fast but tire quickly. These powerful fast acting muscles give the cat the ability to jump to incredible heights relative to body size. The cat however has relatively few "fast-twitch fatigue resistant" muscles. The cat is a sprinter not an endurance runner.
The cat's skeleton has evolved for bursts of speed and agility. The spine is supple. The legs are slender and strong. The long limbs provide excellent leverage. Cats are digitigrades - walking on their toes. The "feet" are long adding to leverage. The longer limbed, more slender cats with long tails for balance are the better climbers. The margay is the top of its class. Below is a short video of Magic jumping. She is slender (less weight relative to size) with long limbs providing excellent leverage. Her father is a serval. The serval has the longest leg length to body size of all the cats, wild and domestic.