It's more common than many people think. A couple is arguing, and in the heat of the moment, the woman calls the police and the man is arrested. Then later, once everyone cools off, the alleged victim is no longer interested in pressing charges. The district attorney (DA) is not required to honor the alleged victim's request, and very often chooses not to.
If a witness or alleged victim does not want to be burdened by the litigation, there are ways for that witness to not testify against the alleged offender. However, it is important to communicate and coordinate this with an experienced defense attorney. This is because there are numerous procedural factors that must be taken into consideration.