Why did the Abbasids not participate in supporting Imam Hussein (PBUH) in Karbala?

Answer

In the name of Allah, be informed, my son, that Imam Hussein (PBUH) is infallible and he does whatever commanded by Allah, the Glorious, his grandfather, the Messenger (PBUH&HF), and his father, Ali Ibn Abi Talib (PBUH). Therefore, he left some and took some accordingly. This is the correct interpretation of the actions of Imam Hussein (PBUH) in his revolution and others, and everything that is mentioned other than that is only speculative judgments. Allah knows best.