Because there are 2 Yazids. One Yazid is Yazid ibn Abi Sufyaan (May Allah be pleased with him), a sahaabi, and the brother of Muawiyah (May Allah be pleased with him). The other Yazid is Yazid ibn Muawiyah, the one who caused all the carnage you mentioned above. When people say Yazid radi allahu anhu, they are referring to Muawiyah radi allahu anhu's BROTHER, not his wayward son.