Rubber's trueuse in modern times is due to its strength and malleability. Common rubber that most people are used to (such as in a tire) is vulcanized. The process of vulcanization is heating natural rubber, a product of rubber trees, with sulfur to make it much harder and durable. Natural rubber is more malleable and becomes softer at higher temperatures and very brittle at low temperatures.
To attempt an answer to your question, the strength of a material has a lot to do with what you can use it for. For example, natural rubber was used by American Natives (Aztecs) for rubber playing balls. Modern vulcanized rubber is much stronger and can be used in the durable use as tires. We now use mostly synthetic rubber in most products.