According to rahyafte (the missionaries and converts website):There are, for example, verses about Imam Hassan (AS) and Imam Hussein (AS), and some of them also refer to the status of Imam Ali (AS) and Hazrat Zahra (SA). Some of the examples are as follows:
1- Surah Al-Insan: According to credible historical accounts and Hadiths, the verses of Surah Al-Insan are not directly about the virtues of Imam Hassan (AS) and Imam Hussein (AS), although their revelation is about their illness. Urge by the Holy Prophet (PBUH), Imam Ali (AS) and Hazrat Zahra (SA) make a pledge to fast for three days if Hassan and Hussein recover from the illness. When the illness was gone, they did what they had pledged. On the first day at the time of Iftar (breaking the fast), a poor man came and asked for food. They gave what they had for Iftar to the poor man. The same thing happened on the second and third night and they gave their food to an orphan and a prisoner. The part of the Surah about Imam Hassan (AS) and Imam Hussein (AS) is the one that highlights their status, which is such that Imam Ali (AS) and Hazrat Zahra (AS) get worried about their health and make a pledge to fast if they get healed.
2- Verse 33 of Surah Al-Ahzab, in which God says, “O family of the House, Allah only wishes to distance fault from you, and to cleanse you, and to purify you abundantly.” History says that the Holy Prophet (PBUH) was in the house of Hazrat Zahra (SA) one day. He told Hazrat Zahra (SA) to bring his Aba (cloak). Then the Prophet (PBUH) went under the Aba and invited Imam Ali (AS), Hazrat Zahra (AS) and Hassan (AS) and Hussein (AS) to come under the Aba as well. The Prophet (PBUH) prayed for them and then this verse was revealed.
3- The Verse of Mubahilah in some way proves a special status for Imam Hassan (AS) and Imam Hussein (AS). First, it says the two are the sons of the Holy Prophet (PBUH). The second is the fact that those accompanying the Prophet (PBUH) in the Mubahilah were sacred persons whose prayers were answered.
4- Verse 59 of Surah An-Nisa: God says in this verse: “Believers, obey Allah and obey the Messenger and those in authority among you. Should you dispute about anything refer it to Allah and the Messenger, if you believe in Allah and the Last Day. That is better and the best interpretation.” Who are those in authority? The Holy Prophet (PBUH) said they are Imam Ali (AS), Imam Hassan (AS) and Imam Hussein (AS).
From these we can recognize the sublime status of Imam Hassan (AS), who was an infallible person who knew the Quranic truths and was the Imam of people.
Imam Hassan (AS) became caliph at a time when people had been weary of war and sought to live at ease. Imam (AS) tried to mobilize the people for a battle with Mu’awiya, but only 12,000 people showed up for the war while Mu’awiya had prepared an army of 60,000 men.
Moreover, Mu’awiya deceived Ubaidullah ibn Abbas, one of the commanders of Imam Hassan’s (AS) army, to defect and join the army of Mu’awiya with two-thirds of the Imam’s (AS) soldiers. Mu’awiya could then attack Kufa and defeat Imam Hassan (AS) and his army with ease but did not do it because Imam Hassan (AS) was the caliph and such a move would be interpreted as violating the sanctity of the caliph. So he offered peace to Imam Hassan (AS).
Imam Hassan (AS) knew that if he opted for war, Shia would be killed and no one would remain to explain to others what had happened. So in order to save Muslims’ blood he abandoned the apparent position of caliph.