There is a good reason explaining why gravity is mediated by the graviton. All the other forces (strong, weak and electromagnetic) are quantized. Therefore, it would be really weird not to quantize gravity, wouldn't it? And if one does so, one ends up with a graviton. We also know that its interactions are super super weak. For this reason, it is impossible to observe it. If you find a way and you succeed, I think you may get a Nobel prize!

The extra problem with gravity is that we have no idea about how to quantize it. This is incompatible with general relativity and we need to somehow extend our framework (quantum field theory) to be able to do so. This is today a very active field of research.