"And whoever kills a believer intentionally, his recompense shall be hell, he shall abide therein and God’s wrath shall be on him and his curse, and is prepared for him a great torment”
Muawiyah ibn Abu Sufyan killed respectively ordered the killing of Sahabah, e.g. Amr bin al-Hamiq, Malik bin Ashthar, Hujr bin Adbar, only for the reason that they were followers of Ali ibn Abi Talib.
“Ayesha said: ‘Mu’awiya you killed Hujr and his associates, By Allah! The Prophet told me ‘In the ditch of Adra seven men will be killed, due to this all the skies and Allah will be upset”.
A contemporary Hanafi scholar, Mufti Ghulam Rasul, wrote in his book Subeh al-Sadiq, p.93/94 , that Hujr and his companions were killed because they refused to curse Ali ibn Abi Talib.
Tarikh ibn Asakir, V.12, p.227
Additionally, he instigated the poisoning of the first grandson of the Holy Prophet, Hassan ibn Ali.
“Sho’ubi states that Mu’awiya sent a message to Jada bint al-Ash’ath bin al Qays that if you poison Hasan then I shall marry you to Yazeed and in addition to this I shall give 100,000 dirhams. When Hasan was martyred Judh sent a message to Mu’awiya asking that he fulfil his side of the deal. Mu’awiya sent the money but said “I reject that matter of Yazeed since I want him to remain alive, had this matter not occurred then I would have married you to Yazeed”.
Tadkhirat au Khawwas, p. 192
Mu’awiya reached an agreement with Jada bint al-Ash’ath bin al Qays, namely 100,000 dirhams if she poisons Imam Hasan.
Allamah Zamakshari, Rabi’ ul Abrar, V.4, p. 208
Qatada and Abu Bakr bin Hafs stated that Hasan was administered poison, via his wife Ja’da bint Ashath. One group have said that Mu’awiya have sent Ja’da the poison and upon administering this poison, Ja’da was rewarded”.
Allamah Ibn Abdul Barr, al-Istiab
“This is commonly known among the people that his wife Ja’da administered poison to him upon the orders of Ameer Mu’awiya.”
Maulana Abdur Rahman Jaami, Shawahid un Nubuwwa, p.303
Furthermore, he appointed his son Yazid as the ruler over the Muslims after him, who was the pure evil.
In the light of the above mentioned vers of the Holy Qur'an, the Shia seem right to curse him, by asking Allah swt to deprive him of His mercy. Why can't our Sunni brothers agree to this?