By faction, I am assuming you mean a division within a political movement or organization that splinters from a larger group to form its own independent one.
Based on this definition, there are several reasons why factions are formed. Within a movement, there are certain individuals who might disagree with one or more of the major values or policies, inspiring them to form their own group. They could also feel like they are not being listened to, which causes frustration and the desire to form a faction. They could also disagree not with the values of the primary group but with the methods by which it tries to achieve its goals.
To answer the second part of your question, I will discuss one of two ways in which factions can be dangerous. One reason why factions could be bad is that they can tarnish the unified message of the primary group, thereby creating obstacles to achieving the group’s goals. This means that movements could fail when multiple factions exist.
Another way factions can be dangerous is in the radicalization that often accompanies factions’ ideologies. Because a faction is comprised of more like-minded individuals than a larger group, it is more likely that radical opinions or methods will become platforms of the faction. This happens because insular groups lack the diverse perspectives that tend to moderate extreme opinions. As a result, factions within the government, for example, could cause civil unrest or use violence as a means to an end.