Here's why:
* It refers to a substance, not individual items: We talk about "rubber" as a material, not as distinct, countable pieces.
* You can't use a number with it: You wouldn't say "three rubbers," but rather "three rubber bands" or "three rubber tires."
* It's often used with "a piece of" or "some": "Give me a piece of rubber," "There's some rubber on the floor."
However, there are exceptions:
* When referring to specific objects made of rubber: "He bought two rubbers for his car tires" (referring to the tires themselves).
* In specific contexts: "The band played a rubber song" (referring to a specific type of music).
In most cases, though, you'll treat "rubber" as an uncountable noun.