Final answer:
Sirius Black was thought to be dangerous because he was believed to be a follower of Voldemort, accused of betraying the Potters, and allegedly killed 13 people. However, later in the series, it is revealed that these accusations were based on misunderstandings.
Step-by-step explanation:
Sirius Black is considered dangerous within the Harry Potter series because he was believed to have been a loyal follower of the dark wizard Voldemort and was thought to have betrayed James and Lily Potter to him, leading to their deaths. It was widely thought that he killed 13 people with a single curse, which led to him being sentenced to life imprisonment in Azkaban, the wizarding prison. However, as the series progresses, it becomes clear that Sirius's reputation as a dangerous criminal is a result of misunderstandings and false accusations, and in reality, he is a brave and loyal friend to Harry Potter.