The basic reason for this is that these things gave too much power to British law enforcement agents and reduced the colonists' rights in the judicial system.
Writs of assistance were essentially general search warrants that allowed an officer to search a place at any time to look for evidence of crime. The vice-admiralty courts were courts (located outside the colonies in Halifax) that had no juries to try accused criminals. When combined, these two types of things took away many of the rights that the colonists wanted. These types of things made it easier to find evidence of crime and easier to convict accused people (because a judge appointed by the government would be more likely to convict than a jury from a particular colony). This is why the colonists disliked such things.