This is a correct saying that the infallibility is exclusively limited to prophets and infallible Imams; But Hazrat Abbas (AS) also benefited from this position as much as he could. He had reached to such a position that his heart was the complete mirror of Imam Hussein’s grace, grandeur and perfection. However, he as only thirty three years at the time of his martyrdom and he was able to achieve such important achievements during adolescence and youth. The infallible Imams were all aware of the high spiritual status of Hazrat Abbas (AS) and considered him as a unique gem in the system of being.
source : erfan.ir